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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Multiply and divide powers (the laws of exponents)

Grade 7 Math Worksheet - Building Confidence

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

  1. 5 × 5 (that is 5^2) and 5 × 5 × 5 × 5 (that is 5^4). Esme's worksheet shows 5^2 × 5^4 = 5^?, with the factors written out in two strips. The handwriting is extra neat today. What is the missing exponent?

  2. 2 × 2 (that is 2^2) and 2 × 2 × 2 × 2 × 2 (that is 2^5). Jun flips a puzzle card: 2^2 × 2^5 = 2^?. Its two strips of factors are printed underneath. A gold star waits for the answer. What exponent earns the star?

  3. Kira's math book writes 5^6 ÷ 5^2 = 5^? over a fraction bar, with every factor shown. Someone drew a tiny smile on a 5. What exponent is left after the factors cancel?

  4. Luz writes 7^8 ÷ 7^2 = 7^? over a fraction bar, with the factors on top and below. The pencil is getting very short. What exponent is left after the factors cancel?

  5. Milo's padlock tag reads 4^7 ÷ 4^2 = 4^?, with the factor strips drawn on top and below. The padlock has a tiny smiley sticker. What exponent opens it?

  6. Ren's square quilt has 2^4 patches along each side, so it has (2^4)^2 patches. The figure writes out the factors. It is a very cozy quilt. What exponent makes (2^4)^2 = 2^? true?

  7. Tala's math book shows (4^3)^2 = 4^?, with both copies of 4^3 written out. The page has a doodle of a smiling 4. What is the missing exponent?

  8. Zee packs 6^1 boxes with 6^2 paper stars in each box, so there are 6^1 × 6^2 stars. A few stars are a bit squashed. How many stars are there?

  9. Ari has 3^2 trays with 3^3 bean seeds in each tray. The number of seeds is 3^2 × 3^3. One seed is already trying to sprout. How many seeds are there?

  10. Bo has 2^3 boxes of crayons with 2^4 crayons in each box, so there are 2^3 × 2^4 crayons. The blue ones always go first. How many crayons are there?

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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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