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Properties of Exponents Review - Printable Math Worksheets year 8 - Wayground

Properties of Exponents Review

Amity Geddes

Created by Amity Geddes

18 questions

8th Grade

Math

Updated Oct 2026

Properties of Exponents Review is a Grade 8 mathematics worksheet that helps students apply exponent rules in equivalent-expression and simplification problems. Across 18 questions—17 multiple-choice items and one multiple-select item—students combine powers with the same base, multiply exponents when raising a power to a power, use the zero-exponent rule, and subtract exponents when dividing like bases. They also expand powers as repeated multiplication, simplify products with different bases and the same exponent, work with negative exponents, and solve for an unknown exponent. This free printable worksheet supports review, independent practice, or a formative check after instruction on properties of exponents. The varied items require students to recognize correct rule selection, compare equivalent forms, simplify expressions such as quotients and products, and identify every valid answer in a multiple-select problem. An answer key is included so teachers can quickly check work and use errors to guide reteaching.

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Properties of Exponents Review

Total questions: 18

Name
Class
Date
1.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.

Example: c6 ⋅ c4

a)

add

b)

subtract

c)

multiply

d)

divide

2.
According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d2)5
a)
add
b)
subtract
c)
multiply
d)
divide
3.
Anything raised to a power of zero is always: 
a)
0
b)
1
c)
itself
d)
negative
4.
According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h8 / h3
a)
add
b)
subtract
c)
multiply
d)
divide
5.

Select the expression that is equivalent (equal) to (76)4.

a)

710

b)

72

c)

724

d)

727

6.

What is the correct way to expand  53⋅525^3\cdot5^2  ?

a)

 (5+5+5)(5+5)\left(5+5+5\right)\left(5+5\right)  

b)

 (5×3)(5×2)\left(5\times3\right)\left(5\times2\right)  

c)

 (5×5)(3×2)\left(5\times5\right)\left(3\times2\right)  

d)

 (5⋅5⋅5)(5⋅5)\left(5\cdot5\cdot5\right)\left(5\cdot5\right)  

7.

Select the expression equivalent (equal) to  6863\frac{6^8}{6^3}  .

a)

 6116^{11}  

b)

 656^5  

c)

 6246^{24}  

d)

 6−56^{-5}  

8.

Which expression is equivalent (equal) to  412×7124^{12}\times7^{12}  .

a)

 282428^{24}  

b)

 211221^{12}  

c)

 281228^{12}  

d)

 2814428^{144}  

9.

Which is greater, 26540 or 50?

a)

26540

b)

50

c)

They are the same

d)

Zero is greater

10.

What is the value of x in the equation (73)⋅(7x)=79\left(7^3\right)\cdot\left(7^x\right)=7^9  ?

a)

 33  

b)

 22  

c)

 55  

d)

 66  

11.

Select the expressions that are equivalent (equal) to  (m7⋅m3)4\left(m^7\cdot m^3\right)^4  . (There is more than one answer!)

a)

 m40m^{40}  

b)

 m28⋅m12m^{28}\cdot m^{12}  

c)

 m11⋅m7m^{11}\cdot m^7  

d)

 (m10)4\left(m^{10}\right)^4  

12.

Which expression is equivalent (equal) to  10−3109\frac{10^{-3}}{10^9}  .

a)

 10−1210^{-12}  

b)

 10−610^{-6}  

c)

 10610^6  

d)

 10−2710^{-27}  

13.

Which expression is equivalent (equal) to  (6−4)−262\frac{\left(6^{-4}\right)^{-2}}{6^2}  .

a)

 666^6  

b)

 6−106^{-10}  

c)

 6−86^{-8}  

d)

 6106^{10}  

14.
Rewrite using a positive exponent.
w-13
a)
-w13
b)
1/w13
c)
1/w-13
d)
w13
15.
Simplify:  (x8)(x-5)
a)
x-40
b)
x-13
c)
x13
d)
x3
16.

Which expression is equivalent (equal) to  (123)512−4\frac{\left(12^3\right)^5}{12^{-4}}  .

a)

 121912^{19}  

b)

 121212^{12}  

c)

 121112^{11}  

d)

 12412^4  

17.

 Simplify the expression using the properties of exponents. 

  21x73x4\frac{21x^7}{3x^4}  

a)

 7x37x^3  

b)

 3x33x^3  

c)

 7x117x^{11}  

d)

 18x318x^3  

18.

 Simplify the expression using the properties of exponents.    
 t12u7t2u\frac{t^{12}u^7}{t^2u}  

a)

 t14u8t^{14}u^8  

b)

 t24u7t^{24}u^7  

c)

 t10u7t^{10}u^7  

d)

 t10u6t^{10}u^6  

WaygroundAnswer Key

Properties of Exponents Review

Total questions: 18

1.
a)

add

2.
c) multiply
3.
b) 1
4.
b) subtract
5.
c)

724

6.
d)

 (5⋅5⋅5)(5⋅5)\left(5\cdot5\cdot5\right)\left(5\cdot5\right)  

7.
b)

 656^5  

8.
c)

 281228^{12}  

9.
c)

They are the same

10.
d)

 66  

11.
a)

 m40m^{40}  

, b)

 m28⋅m12m^{28}\cdot m^{12}  

, d)

 (m10)4\left(m^{10}\right)^4  

12.
a)

 10−1210^{-12}  

13.
a)

 666^6  

14.
b) 1/w13
15.
d) x3
16.
a)

 121912^{19}  

17.
a)

 7x37x^3  

18.
d)

 t10u6t^{10}u^6  

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FAQs

What does the Properties of Exponents Review worksheet cover?

This Grade 8 worksheet covers applying exponent properties to simplify and identify equivalent expressions. Its 17 multiple-choice and one multiple-select item ask students to combine exponents for like bases, multiply exponents in a power of a power, apply zero and negative exponent rules, expand powers, and solve for an unknown exponent.

How can I use this worksheet to teach properties of exponents?

Introduce one rule at a time, using the worksheet’s examples such as multiplying like bases, dividing like bases, and raising a power to a power. Then have students explain why each selected expression is equivalent, including why a multiple-select item can have several correct forms and how negative exponents are rewritten with positive exponents.

What mistakes should I watch for on this exponents worksheet?

Watch for students multiplying exponents when multiplying like bases instead of adding them, or adding exponents in a power of a power instead of multiplying them. Other common errors include treating a zero exponent as zero, mishandling negative exponents, subtracting in the wrong direction when dividing, and selecting only one valid expression in the multiple-select item.

How do I assign and grade this Properties of Exponents Review worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key. You can grade digital responses in Wayground or scan students’ printable work with the Wayground for Teachers app.

How can I differentiate this exponents worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the exponent expressions and answer choices easier to read. You can also enable a dyslexia-friendly font or translate the worksheet’s directions and items into another language while keeping the exponent notation visible.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more worksheets at https://wayground.com/en-us/worksheets.

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