Grade 7 · Math

7th grade Multiply and divide powers (the laws of exponents) worksheet

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Multiply and divide powers (the laws of exponents)

Grade 7 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Kira's robot is stuck on 9^4 × 9^6 = 9^?. Its antenna droops a little. What exponent does the robot need?
Luz's craft box holds 3^2 bags with 3^4 beads in each bag, so it holds 3^? beads. The lid barely closes. What is the missing exponent?
Milo's worksheet asks for 6^10 ÷ 6^2 = 6^?. The question is printed in a very serious font. What is the missing exponent?
Ren shares 2^7 pencils equally among 2^3 cups, so each cup gets 2^? pencils. Every cup has a name sticker. What is the missing exponent?
Tala's puzzle card says (4^3)^5 = 4^?. A shiny star sticker is the prize. What exponent earns the star?
Ari writes (3^5)^4 = 3^? at the top of a page. The pencil is freshly sharpened. What is the missing exponent?
Bo's square quilt has 2^3 patches along each side, so it has (2^3)^2 = 2^? patches. It is big enough for a nap. What is the missing exponent?
8.
Kira's padlock tag shows 8^10 ÷ 8^2 and four dial settings. Only one setting is right. Which single power is equal to 8^10 ÷ 8^2?
- 8^12
- 1^8
- 8^5
- 8^8
The art room has 2^9 crayons to share equally among 2^3 tables, so each table gets 2^9 ÷ 2^3. Milo hopes for purple. How many crayons does each table get?
Noah's class folds 3^6 paper stars and packs them equally into 3^2 boxes, so each box holds 3^6 ÷ 3^2 stars. Every star is folded by hand. How many stars are in each box?

7th grade Multiply and divide powers (the laws of exponents) worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Multiply and divide powers (the laws of exponents). Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can write a power as a strip of its factors and count them to multiply powers of the same number (2^3 × 2^4 = 2^7).
I can divide powers by crossing out matching factors (5^6 ÷ 5^2 = 5^4), and I know a power divided by itself is 1.
I can find a power of a power ((3^2)^3 = 3^6), a power of a fraction, and a power of a product ((2 × 5)^3 = 2^3 × 5^3).

Standard: state-only (CCSS 8.EE.A.1)

Words to know

power: A number multiplied by itself, written small and raised: 2^3 = 2 × 2 × 2.

base: The number being multiplied. In 2^3 the base is 2.

exponent: The small raised number. It counts how many factors of the base.

factor: One of the numbers being multiplied. 2 × 2 × 2 has three factors.

strip of factors: A power written out in a row: 2^3 is the strip 2 × 2 × 2.

cancel: A factor on top and the same factor below divide to 1, so cross both out.

Common mistakes

Your child multiplied the small raised numbers when two powers of the same number were multiplied (2^3 × 2^4 as 2^12). Write both powers out as factors together and count them: 3 + 4 = 7 factors of 2.

Your child added the small raised numbers where they should be subtracted (dividing powers) or multiplied (a power of a power). Write the factors out together: for dividing, cross out matching pairs; for a power of a power, count the copies.

Your child divided one small raised number by the other when dividing powers (5^6 ÷ 5^2 as 5^3). Write the factors on top and below a fraction bar, cross out matching pairs and count what is left.

Questions parents ask

What is the most common mistake with multiply and divide powers (the laws of exponents)?

Are these 7th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 7 math

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