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.

   Ren shares 2^7 pencils equally among 2^3 cups, so each cup gets 2^? pencils. Every cup has a name sticker. What is the missing exponent?

   4
3. 3.

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

   15
4. 4.

   Zee's math book asks for (7^2)^6 = 7^?. Someone left a bookmark shaped like a 7. What is the missing exponent?

   12
5. 5.

   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
6. 6.

   Esme's quiz card asks about 6^4 × 6^3. The card has a star in each corner. Which single power is equal to 6^4 × 6^3?

   • 6^1
   • 6^12
   • 6^7
   • 36^7
7. 7.

   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?

   • 3^7
   • 3^3
   • 3^10
   • 9^7
8. 8.

   Kira's padlock tag shows 8^10 ÷ 8^2 and four dial settings. Only one setting is right. Which single power is equal to 8^10 ÷ 8^2?

   • 8^8
   • 1^8
   • 8^5
   • 8^12
9. 9.

   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
10. 10.

    The town library has 10^5 books on 10^3 shelves, the same number on each shelf. Pia wants to read them all. How many books are on each shelf?

    100