Multiply and divide powers (the laws of exponents)

Answer Key - Grade 7 Math Worksheet - Challenge Me

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

1. 1.

   Tala's robot shows 7^6 × 7^3 ÷ 7^5 = 7^?. It taps its foot while it waits. What exponent does the robot need?

   4
2. 2.

   Kira writes (3^2)^5 × 3^4 = 3^? in pencil. The eraser is ready, just in case. What is the missing exponent?

   14
3. 3.

   Milo's robot works out 9^4 ÷ 9^4 = 9^0, and every factor cancels. Its lights blink in surprise. What number is 9^0?

   1
4. 4.

   Noah's combination padlock has a tag that says 6^5 ÷ 6^5 = 6^0. A tiny note says not to panic. What number is 6^0?

   1
5. 5.

   Tala folds a sheet in half 2 times, then 3 more times. The folded piece covers (1/2)^2 × (1/2)^3 of the sheet. It is now very tiny. What fraction of the sheet does it cover?

   1/32
6. 6.

   Ari's puzzle card asks for the value of (2/5)^2 × (2/5)^1. A star sticker is the prize. What is (2/5)^2 × (2/5)^1?

   8/125
7. 7.

   Bo builds a cube with (2 × 5) blocks along each edge, so it uses (2 × 5)^3 blocks. It ends up as tall as a chair. Which expression equals (2 × 5)^3?

   • 10 × 3
   • 2^3 × 5^3
   • 2 × 5^3
   • 2^3 × 5
8. 8.

   Esme's square quilt has (3 × 4) patches along each side, so it has (3 × 4)^2 patches. It is perfect for movie night. Which expression is equal to (3 × 4)^2?

   • 3^2 × 4^2
   • 3^2 × 4
   • 12 × 2
   • 3 × 4^2
9. 9.

   Noah's math book shows (-3)^4 × (-3)^3. A sticky note says "keep the signs". How do you write (-3)^4 × (-3)^3 as a single power of (-3)?

   (-3)^7
10. 10.

    Pia's robot shows (-5)^2 × (-5)^5. It blinks twice while it waits. How do you write (-5)^2 × (-5)^5 as a single power of (-5)?

    (-5)^7