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## Unit 6: Expressions with exponents

About this unit, exponent properties intro.

- Exponent properties with products (Opens a modal)
- Exponent properties with parentheses (Opens a modal)
- Exponent properties with quotients (Opens a modal)
- Exponent properties review (Opens a modal)
- Multiply powers Get 3 of 4 questions to level up!
- Powers of powers Get 3 of 4 questions to level up!
- Divide powers Get 3 of 4 questions to level up!
- Powers of products & quotients (structured practice) Get 4 of 5 questions to level up!
- Powers of products & quotients Get 3 of 4 questions to level up!

## Negative exponents

- Negative exponents (Opens a modal)
- Negative exponent intuition (Opens a modal)
- Negative exponents review (Opens a modal)
- Negative exponents Get 3 of 4 questions to level up!

## Exponent properties (integer exponents)

- Multiplying & dividing powers (integer exponents) (Opens a modal)
- Powers of products & quotients (integer exponents) (Opens a modal)
- Powers of zero (Opens a modal)
- Multiply & divide powers (integer exponents) Get 5 of 7 questions to level up!
- Powers of products & quotients (integer exponents) Get 3 of 4 questions to level up!
- Properties of exponents challenge (integer exponents) Get 3 of 4 questions to level up!

## Scientific notation intro

- Scientific notation examples (Opens a modal)
- Scientific notation example: 0.0000000003457 (Opens a modal)
- Multiplying in scientific notation example (Opens a modal)
- Multiplying & dividing in scientific notation (Opens a modal)
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- Scientific notation Get 5 of 7 questions to level up!
- Multiplying & dividing in scientific notation Get 3 of 4 questions to level up!

## Scientific notation word problems

- Scientific notation word problem: red blood cells (Opens a modal)
- Scientific notation word problem: U.S. national debt (Opens a modal)
- Scientific notation word problem: speed of light (Opens a modal)
- Scientific notation word problems Get 3 of 4 questions to level up!

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## Exponents Worksheets

Reading and writing exponents worksheets.

Our grade 5 exponents worksheets introduce the use of exponents , including the special case of powers of ten .

Sample Grade 5 Exponents Worksheet

## More exponents worksheets

Explore all of our exponents worksheets , from reading and writing simple exponents to negative exponents and equations with exponents.

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- Laws of Exponents

## Laws of Exponents Worksheets

Utilize our printable laws of exponents worksheets as an essential guide for operating on problems with exponents. By steadily practicing these worksheets, students of grade 7, grade 8, and high school will be able to ace their tests in problems using the laws of exponents. Included within this set are worksheets catering to a wide range of topics such as laws of exponents, product rule, quotient rule, power of a power rule, power of a product rule, power of a quotient rule, and a few more. Now, you can access some of our worksheets for free!

Law of Exponents Chart

Explore this chart that works as a handy reference for 7th grade students to brush up their knowledge of the various and important Law of exponents. Explaining Law of exponents with crystal-clear examples, this chart helps them drive home the concept.

Law of Exponents: Product Rule (a m *a n = a m+n )

The product rule is: when you multiply two powers with the same base, add the exponents. Train 8th grade students to rewrite each exponential expression as a single exponent with this set of pdf worksheets. Also, help them develop substantial skills in finding the value of the unknown exponent and MCQ.

Law of Exponents: Quotient Rule ((a m /a n ) = a m-n )

Upgrade your skills in solving problems involving quotient rule by practicing these printable worksheets. The rule states that you can divide two powers with the same base by subtracting the exponents. To facilitate easy practice with numerals and variables, the worksheets are divided into two types.

Law of Exponents: Power of a Power Rule ((a m ) n = a mn )

Look through this set of pdf worksheets to gain sufficient knowledge in rewriting an exponential expression as a single exponent form and solving an exponential equation to find the value of the unknown. Take up the mini MCQ at the end of the worksheets.

Law of Exponents: Power of a Product Rule ((a*b) m = a m *b m )

The power of a product rule states that a term raised to a power is equal to the product of its factors raised to the same power. In order that students apply the rule with confidence and their learning becomes super easy, a variety of problems involving numerals and variables are provided.

Law of Exponents: Power of a Quotient Rule ((a/b) m = (a m /b m ))

The quotient rule states that two powers with the same base can be divided by subtracting the exponents. Follow this simple rule to adeptly and quickly solve exponent problems using the power of a quotient rule. Simplify the questions by performing arithmetic operations and applying the rule.

Evaluate Using Law of Exponents: Mixed review - Type 1

Master evaluating expressions involving numerals with this set of printable worksheets that offers two levels of practice. With eight problems in every page, high school students become well versed in the concept.

Evaluate Using Law of Exponents: Mixed review - Type 2

Employ this stock of pdf worksheets to boost your practice of evaluating expressions involving numerals and variables. The key is for children to use prime factorization and apply the relevant rule of exponents. To arrive at the full and final answer, let them now perform arithmetic operations.

Finding the Missing Variable

Reiterate the concept of finding the value of the missing variable using exponent rules with these printable worksheets. Apply the law of exponents and solve for the variable x in section A; apply the law and solve for the variables x and y in section B.

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Home > Math Worksheets > Word Problems > Exponential Word Problems

## These types of problems have a great deal of application in the real world. They are often used to track population growth among many different wild animal species. This form of math has a wide range of uses in the financial sector it helps millions of people each day make financial decisions for themselves and the companies that they represent. The action of public officials during the latest human pandemic to plague the world (COVID-19) has been be dictated by the exponential spread of the virus. Having a complete understanding of what each exponential graph means allows us to make confident and well thought out decisions. So, you can clearly see that this type of math is not only important, but it saves lives. Exponential word problems are problems involving something that increases at a constant rate. Exponential expressions can also be use to describe three-dimensional shapes. Your students will write expressions involving exponents that describe the given shape situations. They will also write and solve equations involving exponents to solve problems involving constant rates.

This set of worksheets includes word problems that require all four basic mathematical operations (addition, subtraction, multiplication, and division). Problems are at both the basic and intermediate levels, and subject matter includes both money problems and real-world situations (renting hotel rooms, gas mileage, etc.). This set of worksheets contains introductory lessons, step-by-step solutions to sample problems, and a variety of different practice problems, a review, and a quiz. When finished with this set of worksheets, students will be able to solve word problems involving exponents. These worksheets explain how to solve word problems involving exponents. Sample problems are solved and practice problems are provided.

## Get Free Worksheets In Your Inbox!

Exponential word problems worksheets, click the buttons to print each worksheet and answer key., exponential word problems lesson.

This worksheet explains how to write an expression to describe a three-dimensional figure. A sample problem is solved, and two practice problems are provided.

Students will solve word problems requiring them to write and solve exponential equations, and write exponential expressions to describe shapes. Ten problems are provided.

The cost of renting a bike is $54 per day plus $0.09 per mile. If a bike is rented for d days and is driven m miles a day, represent the cost, C, in terms of d and m.

A rectangular tray is twice as long as it is wide. A small border surrounds the tray. The border is a constant 2 feet wide and has an area of 225 square feet. Find the dimensions of the tray.

A rectangular plot is twice as long as it is wide. A small concrete walkway surrounds the plot. The walkway is a constant 3 feet wide and has an area of 165 square feet. Find the dimensions of the plot.

A room is twice as long as it is wide. A small garden surrounds the room. The garden is a constant 4 feet wide and has an area of 304 square feet. Find the dimensions of the room.

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Use these worksheets and task cards to help students learn about exponents. Most worksheets on this page align with Common Core Standard 6.EE.1.

## Exponents w/ Whole Numbers as a Base

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## Exponents w/ Decimal Bases

Practice writing numbers in scientific notation.

Review squared numbers and square roots with these printables.

These worksheets can be used for teaching comparing numbers, ordering, and expanded form.

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## Powers and Exponents Worksheets

Powers and exponents worksheets will produce power and exponents problems for practicing power and exponents problems calculations.These worksheets are very helpful for Kids for basic knowledge. Worksheets give students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation.

## Benefits of Powers and Exponents Worksheets

Powers and exponents worksheets can help students to understand the concept of power and how to apply it to solve more complex math problems that have multiple terms and multiple operations.

Powers and exponents worksheets are interactive and provide several visual simulations. Hence, they enable students to combine fun with learning, creating a positive learning environment. They are also easy to use and free to download.

Powers and exponents worksheets help students off with familiar concepts of division, multiplication, addition and subtraction before adding parentheses and exponents.

## Download Powers and Exponents Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

## ☛ Check Grade wise Exponents Worksheets

- 5th Grade Exponents Worksheets
- Exponents Worksheets 6th Grade
- 7th Grade Exponents Worksheets
- Exponents Worksheets for Grade 8

## Exponents Questions

Exponents questions are provided here to practice various types of questions based on the concept of exponents and powers. These questions are designed according to the latest CBSE/ICSE syllabus for class 8. Practising these questions will help students prepare for their class tests and even final exams.

Let a be any arbitrary number, now a + a = 2a, a + a + a = 3a, and if we multiply it n times we write a + a + a + … n times = na. So this is about adding a number repeatedly, but if we multiply a number repeatedly like a × a = a 2 , a × a × a = a 3 , and a × a × a × a × …n times = a n , then it is called exponents. The number a n is an exponent whose base is a and power is n, and we say it as “a raised to the power n”.

Learn more about exponents and powers .

## Exponents Questions with Solution

Let us solve this practice worksheet on exponents, using the concept and laws of exponents.

Question 1: Simplify the following:

(i) (3/4) 8 × (4/3) 5 (ii) (5/7) 5 × (5/7) –6

(i) (3/4) 8 × (4/3) 5 = (¾) 8 × (¾) –5

= (3/4) 8 – 5 = (3/4) 3

(ii) (5/7) 5 × (5/7) –6 = (5/7) 5 – 6

= (5/7) –1 = 7/5

Question 2: Express each of the following as rational numbers:

(i) (4/5) 4 (ii) (64/81) 3/2 (iii) ( –2/5) –4

(i) (4/5) 4 = 4 4 /5 4 = 256/625

(ii) (64/81) 3/2 = [{64/81} 1/2 ] 3

= [8/9] 3 = 512/729

(iii) ( –2/5) –4 = ( –5/2) 4

Question 3: Simplify each of the following:

(i) [(–2/3) –3 × ( –3/5) 6 ] ÷ (2/3) 5

(ii) (3/4) 5 ÷ (81) 2 × (5/3) 3

(iii) [{( –2/3) 2 } –2 ] –1

= [(–3/2) 3 × ( –3/5) 6 ] × (3/2) 5

= [3 3 + 6 + 5 /(2 3 + 5 × 5 6 )]

= 2 –8 3 14 5 –6

= (3/4) 5 ÷ (3 4 ) 2 × (5/3) 3

= (3/4) 5 × 3 –8 × (5/3) 3

= (3 5 –8 –3 × 5 3 )/4 5

= 3 –6 4 –5 5 3

= ( –2/3) 2 × ( –2) × –1

= ( –2/3) 4

Question 4: A number when divides ( –15) –1 results ( –5) –1 . Find the number.

Let x be the number such that

( –15) –1 ÷ x = ( –5) –1

⇒ –1/15 ÷ x = –⅕

⇒ –1/15 × 1/x = –⅕

⇒ –1/15x = –⅕

⇒ x = ⅓ or 3 –1

Question 5: Simplify:

\(\begin{array}{l}\frac{10 \times 5^{n + 4}+125 \times 5^{n+2}}{3 \times 5^{n+3}+20 \times 5^{n+1}}\end{array} \)

\(\begin{array}{l}=\frac{2 \times 5 \times 5^{n + 4}+5^{3} \times 5^{n+2}}{3 \times 5^{n+3}+2^{2}\times 5 \times 5^{n+1}}\end{array} \)

\(\begin{array}{l}=\frac{2 \times 5^{n + 5}+ 5^{n+5}}{3 \times 5^{n+3}+2^{2} \times 5^{n+2}}\end{array} \)

\(\begin{array}{l}=\frac{5^{n + 5}}{5^{n+2}}\left [ \frac{2 + 1}{3 \times 5+2^{2} } \right ]\end{array} \)

\(\begin{array}{l}=5^{n + 5-n-2}\left [ \frac{3}{15+4 } \right ]\end{array} \)

\(\begin{array}{l}=5^{3}\left [ \frac{3}{19 } \right ]=\frac{375}{19}\end{array} \)

\(\begin{array}{l}\therefore \frac{10 \times 5^{n + 4}+125 \times 5^{n+2}}{3 \times 5^{n+3}+20 \times 5^{n+1}}=\frac{375}{19}\end{array} \)

Question 6: Find the value of p, if 25 (p – 1) + 100 = 5 (2p – 1) .

We have 25 (p – 1) + 100 = 5 (2p – 1)

⇒ 5 (2p – 1) – (5 2 ) (p – 1) = 100

⇒ 5 (2p – 1) – 5 (2p – 2) = 100

⇒ 5 (2p – 2) × (5 – 1) = 100

⇒ 5 (2p – 2) × 4 = 100

⇒ 5 (2p – 2) = 25

⇒ 5 (2p – 2) = 5 2

On comparing the powers,

2p – 2 = 2 ⇒ p = 4

Question 7: Solve for x: 4 x + 2 x – 20 = 0

We have 4 x + 2 x – 20 = 0

⇒ (2 2 ) x + 2 x – 20 = 0

⇒ 2 x + 2 x – 20 = 0

Put 2 x = t, the above equation becomes a quadratic equation

t 2 + t – 20 = 0

⇒ (t + 5)(t – 4) = 0

∴ We get, t = –5 or 4, that is;

2 x = – 5 or 2 x = 4

Since 2 x cannot be negative for any real number x,

2 x = 4 = 2 2

⇒ x = 2 (on comparing the powers on both sides)

Question 8: Solve for x: 4 x – 6(2 x ) + 8 = 0

We have 4 x – 6(2 x ) + 8 = 0

⇒ 2 2x – 6(2 x ) + 8 = 0

Put 2 x = t, we get

t 2 – 6t + 8 = 0

⇒ (t – 4)(t – 2) = 0

∴ We get, t = 2 or 4, that is;

2 x = 2 or 2 x = 4

⇒ x = 1 or 2 (on comparing the powers on both sides)

Question 9: Solve of x: (3/5) 3 × (3/5) –6 = (3/5) 2x – 1

We have, (3/5) 3 × (3/5) –6 = (3/5) 2x – 1

⇒ (3/5) 3 – 6 = (3/5) 2x – 1

Comparing powers on both sides,

⇒ 2x – 1 = –3

Question 10: Simplify: (2 m + 2 – 2 m )/2 m

(2 m + 2 – 2 m )/2 m = 2 m (2 2 – 1)/2 m

= 4 – 1 = 3.

## Video Lesson on Exponents

## Practice Questions on Exponents

1. Find: {(3/2) –1 + ( –2/5) –1 }

2. Simplify:

\(\begin{array}{l}\frac{16 \times 2^{n+1}-4\times 2^{2}}{16 \times 2^{n+2}-2 \times 2^{n+2}}\end{array} \)

3. Solve for x:

(i) 7 x + 1 = 343

(ii) 3 –(x + 1) = 243

(iii) 49 x + 1 = 2(7 x )

4. Simplify: (14 2 – 13 2 ) 5/3

5. Find the value of p: 3 p + 8 = 27 2p + 1 .

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## Exponents Math Worksheets for Kids

Exponents worksheets with writing factors, finding square roots, cube roots, simplyfing exponent expressions and different operations on exponents. Download math worksheet on finding square roots, cube roots and applying different operations on them to practice and score better in your classroom tests.

Parents can download these exponents worksheets for their kids to provide additional practice material at home while teachers can use it as an assignment in the classroom or as a test.

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Exponents Worksheets Create an unlimited supply of worksheets for practicing exponents and powers. Students can solve simple expressions involving exponents, such as 3 3, (1/2) 4, (-5) 0, or 8 -2, or write multiplication expressions using an exponent. The worksheets can be made in html or PDF format (both are easy to print).

Explore all of our exponents worksheets, from reading and writing simple exponents to negative exponents and equations with exponents. What is K5? K5 Learning offers free worksheets, flashcards and inexpensive workbooks for kids in kindergarten to grade 5. Become a member to access additional content and skip ads.

Unit 2 Algebraic expressions. Unit 3 Linear equations and inequalities. Unit 4 Graphing lines and slope. Unit 5 Systems of equations. Unit 6 Expressions with exponents. Unit 7 Quadratics and polynomials. Unit 8 Equations and geometry. Course challenge. Test your knowledge of the skills in this course.

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.

Our exponents worksheets cover reading and writing simple exponents, powers of ten, whole number, fractional and decimal bases, negative exponents and equations with exponents Choose your grade / topic: Grade 5 exponents worksheets Introduction to exponents Reading and writing simple exponents Powers of ten Grade 6 exponents worksheets

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Exponents What are Interactive Worksheets? Interactive Worksheets bring printable worksheets to life! Students can complete worksheets online, and get instant feedback to improve. How do they work? Open an Interactive Worksheet, and create a direct link to share with students.

There are a number of simple exponent rules that make solving the problems on these exponents worksheets easier. The value of any term with an exponent of zero is always equal to one. The value of any term with an exponent of one is always equal to the base.

More exponents worksheets. Explore all of our exponents worksheets, from reading and writing simple exponents to negative exponents and equations with exponents. What is K5? K5 Learning offers free worksheets, flashcards and inexpensive workbooks for kids in kindergarten to grade 5. Become a member to access additional content and skip ads.

Exponential equations refer to algebraic equations with a variable in the exponent position. To solve such problems, you need to evaluate the value of exponents. For example, the equation 4 = 2x is an exponential equation. ... This series of worksheets will work on how to solve for exponential variables in algebraic expressions through the use ...

Section 1.1 : Integer Exponents For problems 1 - 4 evaluate the given expression and write the answer as a single number with no exponents. −62 +4⋅ 32 − 6 2 + 4 ⋅ 3 2 Solution (−2)4 (32 +22)2 ( − 2) 4 ( 3 2 + 2 2) 2 Solution 40 ⋅2−2 3−1 ⋅4−2 4 0 ⋅ 2 − 2 3 − 1 ⋅ 4 − 2 Solution 2−1 +4−1 2 − 1 + 4 − 1 Solution

Utilize our printable laws of exponents worksheets as an essential guide for operating on problems with exponents. By steadily practicing these worksheets, students of grade 7, grade 8, and high school will be able to ace their tests in problems using the laws of exponents.

When finished with this set of worksheets, students will be able to solve word problems involving exponents. These worksheets explain how to solve word problems involving exponents. Sample problems are solved and practice problems are provided. Get Free Worksheets In Your Inbox! Exponential Word Problems Worksheets

Math. Addition (Basic) Addition (Multi-Digit) Algebra & Pre-Algebra. Angles. Area. Comparing Numbers ... Use these worksheets and task cards to help students learn about exponents. Most worksheets on this page align with Common Core Standard 6.EE.1. Exponents w/ Whole ... This file contains 30 task cards with exponent problems on them. 5th ...

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.

Exponents Worksheets are designed to be impactful and engaging. Worksheets encourage students to keep solving problems until they are able to complete entire worksheets without any errors. Repetition: Students can work on the same set of Printable Exponents Worksheets multiple times until they are confident in their knowledge of the concepts.

Get Started Exponents Worksheets Exponents worksheets help students to understand the concept of exponents and powers. Exponents help to represent larger numbers in simpler forms. Such worksheets include exponents with whole numbers, fractional and negative base. Benefits of Exponents Worksheets

Our Exponents and Radicals Worksheets are free to download, easy to use, and very flexible. These Exponents and Radicals Worksheets are a great resource for children in the 4th Grade, 5th Grade, 6th Grade, 7th Grade, and 8th Grade. Click here for a Detailed Description of all the Exponents & Radicals Worksheets.

Determining Slope From a Graph Worksheet; Solve by Factoring Lessons. Solve By Factoring Worksheet; Solve By Using the Quadratic Equation Lessons. Solving Using the Quadratic Formula Worksheet; Solving One Variable Equations; Square Roots and Radicals; Substitution Lessons. Substitution Worksheet; Calculus Help, Problems, and Solutions ...

Powers and Exponents Worksheets Powers and exponents worksheets will produce power and exponents problems for practicing power and exponents problems calculations.These worksheets are very helpful for Kids for basic knowledge.

This Exponents and Radicals Worksheet will produce problems for practicing solving integers with exponents. Worksheets By Topics; Addition; Algebra 1 > Basic Skills; Domain & Range; Equations; Exponents; Inequalities; Linear Equations; Monomials & Polynomials; Quadratic Functions; Radical Expressions;

Let us solve this practice worksheet on exponents, using the concept and laws of exponents. Question 1: Simplify the following: (i) (3/4)8 × (4/3) 5 (ii) (5/7)5 × (5/7) -6 Solution: (i) (3/4) 8 × (4/3) 5 = (¾) 8 × (¾) -5 = (3/4) 8 - 5 = (3/4) 3 = 27/48 (ii) (5/7) 5 × (5/7) -6 = (5/7) 5 - 6 = (5/7) -1 = 7/5

Exponents Math Worksheets for Kids. Exponents worksheets with writing factors, finding square roots, cube roots, simplyfing exponent expressions and different operations on exponents. Download math worksheet on finding square roots, cube roots and applying different operations on them to practice and score better in your classroom tests.