Worksheet

Multiply and divide powers (the laws of exponents)

Grade 7 Math Worksheet - Building Confidence

NameDate

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. 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?

  3. 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?

  4. 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?

  5. Pia's puzzle card says (3^2)^3 = 3^?, with the copies of 3^2 written out. A gold star waits for the answer. What exponent earns the star?

  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. The class shelf has 2^2 rows with 2^4 books in each row, so it holds 2^2 × 2^4 books. Esme has read the funny ones twice. How many books are there?

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Multiply and divide powers (the laws of exponents)

Answer Key - Grade 7 Math Worksheet - Building Confidence

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?

    6

  2. 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

  3. 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?

    6

  4. 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?

    5

  5. Pia's puzzle card says (3^2)^3 = 3^?, with the copies of 3^2 written out. A gold star waits for the answer. What exponent earns the star?

    6

  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?

    8

  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?

    6

  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?

    216

  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?

    243

  10. The class shelf has 2^2 rows with 2^4 books in each row, so it holds 2^2 × 2^4 books. Esme has read the funny ones twice. How many books are there?

    64