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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 - Challenge Me

NameDate

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

  1. Ren's combination padlock shows 3^4 × 3^5 ÷ 3^2 = 3^? on its tag. It is the trickiest padlock in the room. What exponent opens it?

  2. Ari's math book asks for (5^2)^4 × 5^3 = 5^?. It is the last question before lunch. What is the missing exponent?

  3. Kira writes (3^2)^5 × 3^4 = 3^? in pencil. The eraser is ready, just in case. What is the missing exponent?

  4. Esme's worksheet lists four expressions. Exactly one of them is equal to 5^6. The others are sneaky. Which expression is equal to 5^6?

    • 5^12 ÷ 5^2
    • (5^3)^3
    • 5^2 × 5^3
    • 5^2 × 5^4

  5. Jun's robot shows four expressions, but only one is equal to 2^8. It hums while it waits. Which expression is equal to 2^8?

    • (2^4)^2
    • 2^16 ÷ 2^2
    • (2^5)^3
    • 2^2 × 2^4

  6. Tala folds a sheet in half 2 times, then 3 more times. The folded piece covers (1/2)^2 × (1/2)^3 of the sheet. It is now very tiny. What fraction of the sheet does it cover?

  7. Ari's puzzle card asks for the value of (2/5)^2 × (2/5)^1. A star sticker is the prize. What is (2/5)^2 × (2/5)^1?

  8. Bo builds a cube with (2 × 5) blocks along each edge, so it uses (2 × 5)^3 blocks. It ends up as tall as a chair. Which expression equals (2 × 5)^3?

    • 2 × 5^3
    • 2^3 × 5
    • 2^3 × 5^3
    • 10 × 3

  9. Milo's puzzle card says (-2)^3 × (-2)^2. The minus signs look very serious. How do you write (-2)^3 × (-2)^2 as a single power of (-2)?

  10. Noah's math book shows (-3)^4 × (-3)^3. A sticky note says "keep the signs". How do you write (-3)^4 × (-3)^3 as a single power of (-3)?

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

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.

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.

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