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. 4 × 4 (that is 4^2) and 4 × 4 × 4 (that is 4^3). Ari's combination padlock shows 4^2 × 4^3 = 4^? on its tag, with every factor written out below. It looks hopeful. What exponent opens the padlock?

  2. 3 × 3 × 3 (that is 3^3) and 3 × 3 × 3 × 3 (that is 3^4). Bo's robot shows 3^3 × 3^4 = 3^? on its screen, with both strips of factors. It beeps until someone answers. What exponent does the robot need?

  3. 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?

  4. 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?

  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. 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?

  7. 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. 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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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. 4 × 4 (that is 4^2) and 4 × 4 × 4 (that is 4^3). Ari's combination padlock shows 4^2 × 4^3 = 4^? on its tag, with every factor written out below. It looks hopeful. What exponent opens the padlock?

    5

  2. 3 × 3 × 3 (that is 3^3) and 3 × 3 × 3 × 3 (that is 3^4). Bo's robot shows 3^3 × 3^4 = 3^? on its screen, with both strips of factors. It beeps until someone answers. What exponent does the robot need?

    7

  3. 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

  4. 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

  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?

    5

  6. 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

  7. 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

  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. 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?

    128