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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)
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• 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)
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• Negative exponents Get 3 of 4 questions to level up!

Exponent properties (integer exponents)

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• Powers of zero (Opens a modal)
• Multiply & divide powers (integer exponents) Get 5 of 7 questions to level up!
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Scientific notation intro

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Scientific notation word problems

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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 .

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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.

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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
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• 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.

Exponents - Exponents Write Factors and Find Value 1

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