Multiply and divide powers (the laws of exponents)

Answer Key - Grade 7 Math Worksheet

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

1. 1.

   Jun's combination padlock shows 7^5 × 7^8 = 7^? on its tag. It has seen a lot of wrong guesses today. What exponent opens the padlock?

   13
2. 2.

   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?

   6
3. 3.

   Milo's worksheet asks for 6^10 ÷ 6^2 = 6^?. The question is printed in a very serious font. What is the missing exponent?

   8
4. 4.

   Noah's padlock tag reads 9^12 ÷ 9^4 = 9^?. The dials circle hopefully at every guess. What exponent opens the padlock?

   8
5. 5.

   Pia's robot prints 8^12 ÷ 8^3 = 8^? on a long paper strip. It waits with a blinking light. What exponent does the robot need?

   9
6. 6.

   Tala's puzzle card says (4^3)^5 = 4^?. A shiny star sticker is the prize. What exponent earns the star?

   15
7. 7.

   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?

   6
8. 8.

   Jun's math book shows 3^5 × 3^2 and four answers. One page corner is folded down. Which single power is equal to 3^5 × 3^2?

   • 9^7
   • 3^3
   • 3^10
   • 3^7
9. 9.

   Luz's robot offers four answers for 10^8 ÷ 10^2. It spins in a circle while it waits. Which single power is equal to 10^8 ÷ 10^2?

   • 10^4
   • 10^6
   • 10^10
   • 1^6
10. 10.

    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?

    81