Exponents to Numbers Worksheets

How Do You Multiply and Divide Exponents? Multiplying and dividing exponents is very tricky. It requires a strong understanding of how exponents work and what are some of the basic mathematical concepts that can help simplify such equations. There are four basic math operations: addition, subtraction, multiplication, and division. When we are solving exponents, these operations are used altogether in combination. For example, multiplication between two similar constants or variables results in the addition of their powers. Similarly, when the division takes place between two same numbers or variables, the powers are subtracted from each other. This might seem a bit confusing, so let us try and solve these equations one by one. For instance, if you take 2 3 x 2 5 x 2 4 . Then rather than multiplying all these numbers together 12 times, you can simply use the power of addition here, i.e., 2 3+5+4 . This will make 2 12 . The answer you will get is 4096. Similarly, when you have 2 3 / 2 6 . You simply minus 6 from 3, i.e., 2 3-6 , and the answer would be 2 -3 . You can use this multiplication and division of exponents in combination to practice more complicated equations.

Basic Lesson

Demonstrates how to multiple exponents in number sets. Also includes practice problems.

Intermediate Lesson

Step-by-step instruction on how to divide exponents.

Independent Practice 1

10 problems ask for the greatest Multiplying and Dividing Exponents. 10 problems ask for the least common multiple.

Independent Practice 2

20 practice problems that review Multiplying and Dividing Exponents skills. The answers can be found below.

Homework Worksheet

12 problems to reinforce the lessons and practice pages. An example is provided.

10 problems that test Multiplying and Dividing Exponents skills.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

Some functions are together and a derivation walks in. All of the functions but one run & hide. The derivation asks the function "Don't I scare you?" The exponential said, "No, I'm ex " The derivation said " Yeah, but who says I differentiate along x?"

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Multiplying and Dividing Exponents

An exponent shows how many times a given variable or number is multiplied by itself. For example, 6 4 means we are multiplying 6 four times. In the expanded form, it is written as 6 × 6 × 6 × 6. When two exponential terms with the same base are multiplied, their powers are added while the base remains the same. However, when two exponential terms having the same base are divided, their powers are subtracted. Let us learn more about multiplying and dividing exponents in this article.

Dividing Exponents

The laws of exponents make the process of simplifying expressions easier. The basic rule for dividing exponents with the same base is that we subtract the given powers. This is also known as the Quotient Property of Exponents.

Quotient Property of Exponents - Dividing Exponents

How to Divide Exponents?

Dividing exponents becomes easy when we follow the properties of exponents. For example, let us solve the following question in the usual way, 6 5 ÷ 6 3 = (6 × 6 × 6 × 6 × 6)/(6 × 6 × 6 ) = 6 2 . This involves more calculation. However, when we use the laws of exponents, it reduces all these calculations. Let us understand how to divide exponents in different scenarios using the different properties.

Dividing Exponents with Same Base

In order to divide exponents with the same base, we use the basic rule of subtracting the powers. Consider a m ÷ a n , where 'a' is the common base and 'm' and 'n' are the exponents. This 'Quotient property of Exponents' says, a m ÷ a n = a m-n . Now, let us understand this with an example.

Example: Divide 6 5 ÷ 6 3

Solution: We can see that in the given expression, the bases are the same. Using the 'Quotient property of Exponents', we will get, 6 5 - 3 = 6 2 . Therefore the answer is 6 2 .

Dividing Exponents with Different Bases

In order to divide exponents with different bases and the same exponent, we use the 'Power of quotient property', which is, (a/b) m = a m /b m . Consider a m ÷ b m , where the expressions have different bases and the same exponent. For example, let us solve: 12 3 ÷ 3 3 . Using the 'Power of quotient property', this can be solved as, 12 3 ÷ 3 3 = (12 ÷ 3) 3 = 4 3

Power of Quotient Property

Dividing Exponents with Coefficients

In some cases, we need to divide expressions that have coefficients . These coefficients that are attached to their bases can be divided easily in the same way as we divide any other fraction. It should be noted that the coefficients can be divided even if the expressions have different bases.

Example: Divide 12a 7 ÷ 4a 2

Solution: Let us use the following steps to divide expressions with coefficients. In this case, 12 and 4 are the coefficients and the rest are variables.

  • First, we rewrite the expression as a fraction, that is, 12a 7 / 4a 2 .
  • Then we divide the coefficients, that is, 12/4 = 3.
  • After this step, we can apply the quotient property of exponents and solve the variable, that is, a 7 /a 2 = a 7 - 2 = a 5 .
  • So, now we have the coefficient as 3 and the variable is a 5 . This gives the answer as, 3a 5

Multiplying Exponential Terms

Multiplying exponents with the same base and different bases involves certain rules of exponents. Let us understand these in the following section.

Multiplying Exponents with the Same Base

When we multiply two expressions with the same base, we apply the rule, a m × a n = a (m + n) , in which 'a' is the common base and 'm' and 'n' are the exponents. For example, let us multiply 2 2 × 2 3 . Using the rule, 2 2 × 2 3 = 2 (2 + 3) = 2 5 .

Multiplying Exponents with Different Base and Same Power

When we multiply expressions with different bases and the same power, we apply the rule: a m × b m = (a × b) m . For example, let us multiply: 11 4 × 3 4 . This can be solved as, 11 4 × 3 4 = (11 × 3) 4 = 33 4 .

How to Multiply and Divide Fractional Exponents?

In order to multiply and divide fractional exponents, we use the same exponent rules that we apply for whole numbers. Fractional exponents are those expressions in which the powers are fractions, for example, 2 ½ , 6 ¾ , and so on.

Multiplying Fractional Exponents with the Same Base

In order to multiply fractional exponents with the same base, we use the rule, a m × a n = a m+n . For example, let us simplify, 2 ½ × 2 ¾ = 2 (½ + ¾ ) = 2 5/4 .

Dividing Fractional Exponents with the Same Base

For dividing fractional exponents with the same base, we use the rule, a m ÷ a n = a m-n . For example, let us solve, 3 3/2 ÷ 3 1/2 . Using the rule, we get, 3 (3/2 - 1/2) = 3 1 = 3.

How to Multiply and Divide Exponents With Variables?

The rules which are used in numbers are also used in exponents with variables. Let us recollect them and then use them in the following examples:

  • a m × a n = a m+n
  • a m × b m = (a × b) m
  • a m ÷ a n = a m-n
  • a m ÷ b m = (a ÷ b) m

Variable as the Base

Let us see how to use these rules when the base is a variable. For example, solve: y 2 × (2y) 3

We will apply the rule: a m × b m = (a × b) m , y 2 × (2y) 3 = y 2 × 2 3 × y 3 = 2 3 × y (2+3) = 8y 5

Variable as the Exponent

Let us see how to use the rules when the exponent is a variable. For example, solve: 5 (2x -1) ÷ 5 (x + 1)

We will apply the rule: a m ÷ a n = a m-n , we get 5 (2x -1 - x - 1) = 5 (x -2)

Tips on Multiplying and Dividing Exponents

  • a 0 = 1[ since a m ÷ a m = 1 = a m-m = a 0 ]
  • It should also be noted that a negative exponent can be converted to a positive exponent by writing the reciprocal of the number. For example, 6 -3 can be written as 1/6 3 .
  • If we multiply two exponents with the same base then their powers will add.
  • If we divide two exponents with the same base then their powers will subtract.

Related Topics

  • Rational Exponents
  • Irrational Exponents

Multiplication and Division of Exponents Examples

Example 1: Find the value of the expression, 16 8 × 16 3

Solution: Using the exponent rule for multiplying exponents, we can solve the given expression. According to the 'Product property of exponents', a m × a n = a (m + n)

Applying this rule, we get, 16 8 × 16 3 = 16 8 + 3 = 16 11

Example 2: Find the value of the expression \(\dfrac{a^{(n-2)}}{a^{(2n-4)}}\)

Solution: Applying the rules for dividing exponents, we can solve the given expression. According to the 'Quotient property of exponents', a m ÷ a n = a m-n . So, the given expression will be,

\(\dfrac{a^{(n-2)}}{a^{(2n-4)}}\) = a (n - 2 - 2n + 4)

= a (n - 2 - 2n + 4) = a (2 - n)

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exponents with multiplication and division worksheet answers

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Practice Questions on Multiplying And Dividing Exponents

Faqs on multiplying and dividing exponents, how do you multiply and divide exponents.

In order to multiply and divide exponents, we use a set of exponent rules. When two exponential terms with the same base are multiplied, their powers are added while the base remains the same. For example, let us multiply, 6 3 × 6 5 = 6 (3 + 5) = 6 8 . However, when two exponential terms having the same base are divided, their powers are subtracted. For example, 7 8 ÷ 7 5 = 7 3 . Similarly, there are other rules that help to simplify exponents easily.

What are the Rules for Dividing Exponents?

There are a few exponent rules that help in the division of exponents. These rules also help in simplifying numbers with complex powers involving fractions , decimals , and roots. For example, in order to divide the numbers or variables with the same base, we apply the rule: a m ÷ a n = a m-n . To divide the numbers or variables with different bases, we apply the rule: a m ÷ b m = (a ÷ b) m

How do you Solve Exponents in Parentheses?

The exponents inside parentheses can be solved using the identity (a m ) n = a mn . For example, (4 2 ) 3 = 4 (2 × 3) = 4 6 = 4096

Can we Distribute Exponents Over Division?

Yes, we can distribute exponents over division . For example, (7/2) 3 = 7 3 ÷ 2 3 = 343/8

How to Multiply and Divide Negative Exponents?

When we multiply and divide negative exponents , we follow the same rules that are used for positive exponents. For example, we use the property: a m ÷ a n = a m-n , to solve: 2 -3 ÷ 2 -4 . This will be: 2 (-3-(-4)) = 2 (-3 + 4) = 2 1 = 2. Observe the rule of simplification of integers which changes the sign after the brackets are opened. It should also be noted that a negative exponent can be converted to a positive exponent by writing the reciprocal of the number. For example, 7 -3 can also be written as: 1/7 3 . This means that if we need to divide expressions that have negative exponents, we can simply move the base to the other side of the fraction bar. For example, if we have 4 -2 in the denominator of a fraction, we can move it to the numerator. This means, y -2 /y -3 = y 3 /y 2 = y 3 - 2 = y 1 = y.

How to Divide Exponents with Different Powers?

In order to divide exponents with different powers, but the same bases, we subtract the given powers. The property which is used here is, a m ÷ a n = a (m-n) . For example, let us divide the exponents, 8 6 ÷ 8 4 . After applying the Quotient property of exponents, we get, 8 6 - 4 = 8 2

How to Divide Exponents with Fractions?

In order to divide exponents with fractions, we use the same rule that is used for whole numbers , that is, a m ÷ a n = a m-n . For example, let us divide the following exponents, 2 3/4 ÷ 2 1/2 = 2 3/4 -1/2 = 2 1/4 .

How to Divide Exponents with Different Bases and Same Powers?

In order to divide exponents with different bases and the same powers, we apply the 'Power of Quotient Property' which is, a m ÷ b m = (a ÷ b) m . For example, let us divide, 14 3 ÷ 2 3 = (14 ÷ 2) 3 = 7 3 .

How to Divide Exponents with Negative Bases?

When we need to divide exponents with negative bases, the exponent rules remain the same. For example, let us divide (-4) 8 ÷ (-4) 2 = (-4) 8 - 2 = (-4) 6

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Exponent Worksheets

This assortment of printable exponents worksheets designed for grade 6, grade 7, grade 8, and high school is both meticulous and prolific. As well as cracking the distinctly advantageous aspects of exponents, a unique math shorthand used to denote repeated multiplication, students gain an in-depth knowledge of parts of an exponential notation, converting an expression with exponents to a standard or an expanded form, and applying laws of exponents while solving an exponential equation. Some of our worksheets are absolutely free of cost.

Base and Exponents - Type 1

Base and Exponents - Type 1

Keep 6th grade students fully informed of the significance of an exponential notation with this set of worksheets. These exercises help them ably identify its parts and express a numeral in an exponential form.

  • Download the set

Base and Exponents - Type 2

Base and Exponents - Type 2

Become adept at identifying the base and exponents from an exponential notation and writing the given numerals and variables in an exponential form with this bunch of pdf worksheets for grade 7.

Exponential Form and Expanded Form - Type 1

Exponential Form and Expanded Form - Type 1

These printable worksheets hammer home this concept: an exponent denotes the number of times a base is multiplied by itself. The task here is to express numbers in expanded and exponential forms.

Exponential Form and Expanded Form - Type 2

Exponential Form and Expanded Form - Type 2

Augment your skills in converting between expanded and exponential forms with this 7th grade pdf practice set. The questions here include variable bases in integer, fraction, and decimal dimensions.

Exponential Form and Standard Form | Integers

Exponential Form and Standard Form | Integers

Hone in on expanding and evaluating an exponential expression in part A, rewriting an integer in exponential form in part B, and expressing a numeral as prime powers in part C of this practice set.

Exponential Form and Standard Form | Fractions

Exponential Form and Standard Form | Fractions

Encompassing three different exercises, each worksheet in this all-inclusive set provides children ample practice in expressing positive and negative fractions in standard, expanded, and exponential forms.

Product of Power of Primes

Product of Power of Primes

Become conversant with applying the method of prime factorization to express three-digit and four-digit integers as a product of its prime factors raised to appropriate powers with these 6th grade worksheets.

Reciprocals and Inverses of Exponents

Reciprocals and Inverses of Exponents

Introduce 8th graders to the concept of reciprocals or multiplicative inverses of an exponential expression involving integer and fractional bases and positive and negative exponents with these pdf worksheets.

Finding the Missing Base or Exponent | Integers

Finding the Missing Base or Exponent | Integers

This set of printable worksheets for students of grade 8 and high school features monomial and exponential equations with a variable 'x'. Solve for x by factorizing the constants and forming an equation with like bases.

Finding the Missing Base or Exponent | Fractions

Finding the Missing Base or Exponent | Fractions

Work your way through these exercises incorporating fractional bases and integer exponents, and become proficient in finding the missing base or exponent in every given equation applying relevant properties.

Operations with Exponents | Integers

Operations with Exponents | Integers

Looking to extend your practice with the four basic math operations in an exponents' scenario: addition, subtraction, multiplication, and division? Here are materials that more than meet your requirement.

Operations with Exponents | Fractions

Operations with Exponents | Fractions

Master adding, subtracting, multiplying, and dividing expressions with exponents with these pdf worksheets. Follow the order of operations, apply the power of a quotient rule, and evaluate each expression.

Laws of Exponents Worksheets

Laws of Exponents Worksheets

This huge stock of printable worksheets includes a chart that lets students explore the various laws of exponents and a multitude of practice worksheets that help them apply these laws to find the missing exponents, evaluate an exponential expression, and solve an exponential equation.

(46 Worksheets)

Evaluating Numerical Expressions with Exponents Worksheets

Evaluating Numerical Expressions with Exponents Worksheets

Streak ahead with our pdfs featuring adequate exercises in simplifying arithmetic expressions with exponential notations involving fractions, decimals, and integers raised to positive and negative powers using the PEMDAS, BODMAS, or BEDMAS.

(59 Worksheets)

Evaluating Exponential Functions Worksheets

Evaluating Exponential Functions Worksheets

These evaluating exponential functions worksheets should be your pick if you are looking for substantial practice. Simply plug in the value of x in the function that is in the exponential form: f(x)=b x and evaluate.

(6 Worksheets)

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Multiplying Exponents (All Positive) (A)

Welcome to The Multiplying Exponents (All Positive) (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2016-01-19 and has been viewed 385 times this week and 1,739 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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High School Math : Multiplying and Dividing Exponents

Study concepts, example questions & explanations for high school math, all high school math resources, example questions, example question #1 : simplifying exponents.

Simplify the following expression.

exponents with multiplication and division worksheet answers

In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.

exponents with multiplication and division worksheet answers

Now, simplifly the numerals.

exponents with multiplication and division worksheet answers

Example Question #2 : Simplifying Exponents

Simplify the following expression. 

exponents with multiplication and division worksheet answers

Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents. 

exponents with multiplication and division worksheet answers

Example Question #3 : Simplifying Exponents

exponents with multiplication and division worksheet answers

Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents. 

exponents with multiplication and division worksheet answers

We also recall that for negative exponents,

exponents with multiplication and division worksheet answers

Simplify the following exponent expression:

exponents with multiplication and division worksheet answers

Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:

exponents with multiplication and division worksheet answers

Multiply the exponents:

exponents with multiplication and division worksheet answers

Simplify the expression:

exponents with multiplication and division worksheet answers

First simplify the second term, and then combine the two:

exponents with multiplication and division worksheet answers

Example Question #6 : Simplifying Exponents

exponents with multiplication and division worksheet answers

Cannot be determined from the given information.

Rewrite each side of the equation to only use a base 2:

exponents with multiplication and division worksheet answers

The only way this equation can be true is if the exponents are equal.

exponents with multiplication and division worksheet answers

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Course: Algebra 1   >   Unit 11

  • Multiplying & dividing powers (integer exponents)

Multiply & divide powers (integer exponents)

  • Powers of products & quotients (integer exponents)
  • Properties of exponents challenge (integer exponents)

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Multiplying and Dividing exponents

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PEMDAS Problems Worksheets 5th Grade

Welcome to our PEMDAS Problems page. Here you will find our range of Math sheets which will help your child learn to use parentheses (brackets) and exponents (powers). There are also lots of sheets to help you practice and master PEMDAS.

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What is pemdas.

  • All Worksheets
  • Using Parentheses Worksheets
  • Using Exponents Worksheets

Using Parentheses and Exponents Worksheets

  • Order of Operations Worksheets

PEMDAS Challenges & Games

  • Harder PEMDAS Worksheets
  • More Recommended Resources

PEMDAS Problems Online Quiz

Pemdas problems worksheets and help.

Here you will find a range of 5th grade math sheets which will help your child learn to use parentheses and exponents, and practice PEMDAS with a range of equations.

The sheets are arranged in order of difficulty with the easiest sheets first.

Using these sheets will help your child to:

  • learn to use parentheses (brackets) and understand how they work;
  • learn to use exponents (powers) and understand how they work.
  • practice using PEMDAS to solve a range of different problems involving parentheses, exponents, as well as addition, subtraction, multiplication and division.

These pemdas problems are aimed at a 5th and 6th grade level.

PEMDAS (sometimes referred to as PEMDAS, BEDMAS or BODMAS) is a mathematical acronym to help you understand how calculations work.

The acronym refers to the order in which any calculation shold be done, and is typically introduced at around the 5th grade level.

The acronym stands for the following:

  • P = Parentheses (Brackets)
  • E = Exponents
  • D = Division
  • M = Multiplication
  • A = Addition
  • S = Subtraction

One popular way to remember the PEMDAS rule is the saying:

'Please Excuse My Dear Aunt Sally'.

However, the PEMDAS rule is not quite so straightforward as it seems.

If you would like help using this rule and looking at some worked examples, follow the link below.

  • PEMDAS Rule Support Page

The sheets below do use the PEDMAS rule, but it is not necessary for you to be familiar with it in order to complete the worksheets.

The worksheets below gradually introduce parentheses and exponents in a simple way so that your child can (hopefully) quickly grasp these concepts before they start solving trickier pemdas problems.

Pemdas Problems - Using Parentheses (Brackets) Worksheets

  • Using Parentheses Sheet 5:1
  • PDF version
  • Using Parentheses Sheet 5:2

Pemdas Problems - Using Exponents (Powers) Worksheets

  • Using Exponents Sheet 5:1
  • Using Exponents Sheet 5:2

Using Parentheses & Exponents Worksheets

  • Using Parentheses & Exponents Sheet 5:1
  • Using Parentheses & Exponents Sheet 5:2

Using Parentheses and Exponents Walkthrough Video

This short video walkthrough shows several problems from our Using Parentheses & Exponents Sheet 5:1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

PEMDAS Problems - Order of Operations Worksheets

The sheets below use PEMDAS to work out a range of calculations.

The first series of sheets are a great resource for students who are just learning the rule.

The second series of sheets are good for stretching and challenging more able students.

Pemdas Problems - Order of Operations worksheets

  • Order of Operations Sheet 1
  • Order of Operations Sheet 2
  • Order of Operations Sheet 3

PEMDAS Challenges Worksheets

  • PEMDAS Challenges Sheet 1
  • PEMDAS Challenges Sheet 2
  • PEMDAS Challenges Sheet 3

PEMDAS RULE GAME

The PEMDAS rule game is a game which involves using brackes, multiplication and addition or subtraction.

The aim of the game is to place digit cards in the pemdas game boards to get as close to the given target as possible.

PEMDAS GAME

Grade: 5th Grade + Number of players: any. Learning skills: learning PEMDAS and reasoning skills.

  • Pemdas Game Board: addition and multiplication
  • Pemdas Game Board: subtraction and multiplication
  • Instructions
  • Digit Cards 0-9 Sheet 1
  • Digit Cards 0-9 Sheet 2

Looking for something harder?

The sheets in this section are at a harder level than those on this page.

  • 6th Grade Order of Operations

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Fifth Grade Number Worksheets

Here you will find a range of Free Printable 5th Grade Number Worksheets.

  • use place value with up to 3 decimal places;
  • understand how to use exponents (powers) of a number;
  • understand and use parentheses (brackets);
  • understand and use multiples and factors;
  • extend their knowledge of prime and composite (non-prime) numbers up to 100;
  • know and be able to use the PEMDAS (or PEDMAS) rule.

All the Free 5th Grade Math Worksheets in this section are informed by the Elementary Math Benchmarks for 5th Grade.

  • 5th Grade Place Value to 3dp
  • Balancing Math Equations

Ordering Large Numbers and Decimals to 3dp

The sheets in this section involve ordering lists of decimals to 3 decimal places.

There are sheets with decimals up to 10, and also sheets with numbers from -10 to 10.

Each sheet is carefully graded and comes with an answer sheet provided.

  • Ordering Large Numbers up to 100 million
  • Ordering Decimals to 3dp

Fifth Grade Math Games

Here you will find a range of free printable 5th Grade Math games.

All children like to play Math games, and you will find a good range of Grade 5 Math Games here for your child to play and enjoy.

The following games involve different 5th Grade Math activities which you and your child can enjoy together.

  • Math Games 5th Grade

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill at using PEMDAS to solve a range of math problems here.

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Division of Exponents Worksheets

This is a core skill in most science labs. It lays a good foundation to work with operations in scientific notation. While this is very intimidating when you first see a problem, students quickly learn that this skill is quite simple. The most difficult part of this unit is understanding integer operations especially with negative values. Remind students that subtracting a negative value by another negative makes the sign flip and it becomes a negative plus a plus. This set of worksheets and lessons help students understand how to divide values that contain exponents. We introduce binomials in this section. The math is the same, you just need to split them up and stay organized all the way through the problem.

Aligned Standard: 8.EE.A.1

  • Simple Lesson - This includes the use of negative numbers as well.
  • Complex Lesson - A two dimensional problem is given (numerals and variables).
  • Guided Lesson - Each problem has a different level of difficulty for you.
  • Guided Lesson Explanation - We practice using the quotient rule over the series.
  • Simple Quotients of Exponents Worksheet - As basic as it gets.
  • Difficult Worksheet - I would only have students that have mastered the basic skills start to work with these problems.
  • Answer Keys - These are for all the unlocked materials above.

Algebra Based Quotient Rule Worksheets

It's a lot of combine like factors and solve.

  • Practice 1 - There are mixed binominals. The same basic strategy applies, but now you have two variables to contain.
  • Practice 2 - Don't forget about the whole numbers. We use larger constants here.
  • Practice 3 - Solve for the following. Do not disregard the constant values before you finish.
  • Practice 4 - Simplify for the following. Students find it more difficult to work with problems that lack base numbers.

Multiple Variable Quotients of Exponents Worksheets

Simplify these as far as you can.

  • Practice 1 - Simplify the following exponent problems. Remember that all of the answers will contain positive exponents.
  • Practice 2 - Everything is positive. Just trust me on that.
  • Practice 3 - Know when to subtract and add. There will be some negative values, but it will all work out in the end.
  • Practice 4 - Write your answers using positive exponents only.

Positive and Negative Quotients of Exponents Sheets

Simplify these guys. Remember that all of your answers will be positive.

  • Sheet 1 - A nice mix for reviews. You might want to review how negative and positive integers interact.
  • Sheet 2 - Some movement here is great. Remember that minus a minus is a plus.
  • Sheet 3 - Solve for the following division of exponents.

Additional Division Based Problems Sheets

Practice makes perfect!

  • Sheet 2 - You can't get much too closer than solving these.
  • Sheet 3 - This worksheet covers a lot of ground.
  • Sheet 4 - Another one that gets easier as it goes along.
  • Sheet 5 - Remind yourself how to line up the dividend and divisor.
  • Sheet 6 - This should be a quick one for your students.

Difficult Problems

Again, these are for students that have a good handle on what they are doing.

  • Practice 2 - These really step up the level of critical thinking.
  • Practice 3 - We would suggest planning how you will perform these calculations before you attempt them.

Tips for Dividing Exponents

Exponents are a quick way to display very large or small values using the base ten number system. The value 100,000 can be written as 10 4 . The 4 represents the number of zeroes found after 10.

The lesson will be going over a key rule in the world of exponents which is related to the quotient rule. This rule can be used for dividing exponents. When exponents have the same base and we are trying to find their difference, we simply need to find the difference between the exponents. It follows the flow: (a b / a c ) = a b - c . Let's try understanding this with a few examples.

Suppose that you have the responsibility of handing out the jellybeans at a party. You have around 1,000,000,000 jellybeans to divide evenly among 10,000 people. You already know that you need to divide the numbers. But there is an easier way of doing it rather than using the long division method. We can use exponents.

1,000,000,000 has 9 zeros which can be written as 10 9 and 10,000 can be written as 10 4 . What we need to do here is divided 10 9 with 10 5 . It will help us determine how many jellybeans with be divided among the members.

The exponent rule of quotient dictates that we can subtract the exponent below from the upper exponent considering the base is the same.

10 9 - 10 4 = 10 5 . Our final answer is 10 5 which means that every person will get 100,000 jellybeans. That is a lot of jellybeans for a single individual.

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  3. A Nice Exponents Multiplication Problem

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  5. LESSON 7-3 MULTIPLICATION PROPERTIES OF EXPONENTS

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COMMENTS

  1. Multiplying and Dividing Exponents Worksheets

    This worksheet explains how to multiply exponents with the same base. A sample problem is solved and a practice problem is provided. Multiplying and Dividing Exponents Students will multiply and divide exponents, as well as express whole numbers in exponential form. Ten problems are provided. Practice with Exponents

  2. PDF Exponents and Division

    Exponents and Division Date_____ Period____ Simplify. Your answer should contain only positive exponents. 1) 54 5 2) 3 33 3) 22 23 4) 24 22 5) 3r3 2r 6) 7k2 4k3 7) 10 p4 6p 8) 3b 10 b3 9) 8m3 10 m3 ... Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com.

  3. Algebra 1 Worksheets

    Our Exponents Worksheets are free to download, easy to use, and very flexible. These Exponents Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Click here for a Detailed Description of all the Exponents Worksheets. Quick Link for All Exponents Worksheets Click the image to be taken to that Exponents Worksheet.

  4. Multiplying and Dividing Exponents Worksheets

    Multiplying and dividing exponents is very tricky. It requires a strong understanding of how exponents work and what are some of the basic mathematical concepts that can help simplify such equations. There are four basic math operations: addition, subtraction, multiplication, and division.

  5. Algebra 1

    This Algebra 1 - Exponents Worksheet produces problems for working with Exponents with Multiplication and Division. Include These Types of Problems Both Multiplication and Division Only Multiplication Only Division Include These Types of Exponents Both Positive and Negative Exponents Only Positive Exponents Language for the Exponents Worksheet

  6. PDF Exponents and Multiplication

    Exponents and Multiplication Date_____ Period____ Simplify. Your answer should contain only positive exponents. 1) 42 ⋅ 42 2) 4 ⋅ 42 3) 32 ⋅ 32 4) 2 ⋅ 22 ⋅ 22 5) 2n4 ⋅ 5n4 6) 6r ⋅ 5r2 7) 2n4 ⋅ 6n4 8 ... Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com.

  7. Free exponents worksheets

    (These determine the number of problems) Difficulty level: Easy level Medium level Type of problem: Solve. For example, solve 4 3. Write repeated multiplications using exponents. For example, write 24 × 24 × 24 × 24 × 24 as 24 5. You don't need to solve.

  8. Multiplying and Dividing Exponents

    In order to divide exponents with different bases and the same exponent, we use the 'Power of quotient property', which is, (a/b) m = a m /b m. Consider a m ÷ b m, where the expressions have different bases and the same exponent. For example, let us solve: 12 3 ÷ 3 3.

  9. Exponents Worksheets

    This assortment of printable exponents worksheets designed for grade 6, grade 7, grade 8, and high school is both meticulous and prolific. As well as cracking the distinctly advantageous aspects of exponents, a unique math shorthand used to denote repeated multiplication, students gain an in-depth knowledge of parts of an exponential notation, converting an expression with exponents to a ...

  10. Multiplying Exponents (All Positive) (A)

    Welcome to The Multiplying Exponents (All Positive) (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2016-01-19 and has been viewed 28 times this week and 864 times this month.

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    Free practice questions for High School Math - Multiplying and Dividing Exponents. Includes full solutions and score reporting.

  12. PDF Exponent Operations Worksheet #1

    Exponent Operations Worksheet #1 Test Study Guide Multiplication of Repeated Bases 1.) If two expressions have the same base, what happens to the exponents when the expressions are multiplied? __________________________________________________________________________________________

  13. Exponents Worksheets: Multiplication with Exponents

    Multiplication with Exponents Math Worksheets Go Ad Free! Core Math Worksheets Addition Worksheets Subtraction Worksheets Multiplication Worksheets Division Worksheets Fact Family Worksheets Long Division Worksheets Negative Numbers Exponents Worksheets Order of Operations Worksheets Fraction Worksheets Fractions Worksheets Graphic Fractions

  14. Multiplying & dividing powers (integer exponents)

    David Severin. 2 years ago. The rule for dividing same bases is x^a/x^b=x^ (a-b), so with dividing same bases you subtract the exponents. In the case of the 12s, you subtract -7- (-5), so two negatives in a row create a positive answer which is where the +5 comes from. In the x case, the exponent is positive, so applying the rule gives x^ (-20 ...

  15. Algebra 1

    Operations with Exponents Worksheets. This Algebra 1 - Exponents Worksheet produces problems for working with different operations with exponents. You may select from exponents with multiplication or division and products or quotients to a power.

  16. PDF Properties of Exponents

    Your answer should contain only positive exponents. 1) 2 m2 ⋅ 2m3 4m5 2) m4 ⋅ 2m−3 2m 3) 4r−3 ⋅ 2r2 8 r 4) 4n4 ⋅ 2n−3 8n 5) 2k4 ⋅ 4k 8k5 6) 2x3 y−3 ⋅ 2x−1 y3 4x2 ... Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. Title: Properties of Exponents

  17. Multiply & divide powers (integer exponents)

    Lesson 1: Exponent properties review Multiplying & dividing powers (integer exponents) Multiply & divide powers (integer exponents) Math > Algebra 1 > Exponents & radicals > Exponent properties review Multiply & divide powers (integer exponents) Google Classroom Simplify. Rewrite the expression in the form a n . a − 13 a − 6 = Stuck?

  18. PDF Exponents Final Review

    statements. Do not use calculators. c. (−5)3 ÷ (−5)2 = 5 d. 2 × 4 = 6 and b. = c. √− d. 2 a. = × × b. = = 11 × × × h. × 2. Write the volume of each prism using exponents instead of repeated multiplication. a. = b. = 3. Use exponent laws to simplify your answers. a. = b. =

  19. Multiplying and Dividing exponents worksheet

    Liveworksheets transforms your traditional printable worksheets into self-correcting interactive exercises that the students can do online and send to the teacher. ... Math (1061955) Main content: Multiplying and Dividing exponents (simplify) (1217157) 12 questions, matching exercise. Loading ad... Share / Print Worksheet. Google Classroom ...

  20. Exponents and Radicals Worksheets

    This Exponents and Radicals Worksheet produces problems for working with Exponents with Multiplication and Division. Include These Types of Problems Both Multiplication and Division Only Multiplication Only Division Include These Types of Exponents Both Positive and Negative Exponents Only Positive Exponents

  21. PEMDAS Problems Worksheets

    PEMDAS Problems Worksheets and Help. Here you will find a range of 5th grade math sheets which will help your child learn to use parentheses and exponents, and practice PEMDAS with a range of equations. The sheets are arranged in order of difficulty with the easiest sheets first. learn to use parentheses (brackets) and understand how they work;

  22. Division of Exponents Worksheets

    Practice 1 - Simplify the following exponent problems. Remember that all of the answers will contain positive exponents. Practice 2 - Everything is positive. Just trust me on that. Practice 3 - Know when to subtract and add. There will be some negative values, but it will all work out in the end.

  23. multiplication and division exponent rules worksheet

    This task card activity includes 12 questions where students will need to use their knowledge of exponent rules for multiplication and division to answer each question. Students will be writing exponents in expanded form, multiplying with exponents, dividing with exponents, and power to power. There are two versions included: color and black ...