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.

   Ren's combination padlock shows 3^4 × 3^5 ÷ 3^2 = 3^? on its tag. It is the trickiest padlock in the room. What exponent opens it?

   7
2. 2.

   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
3. 3.

   Ari's math book asks for (5^2)^4 × 5^3 = 5^?. It is the last question before lunch. What is the missing exponent?

   11
4. 4.

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

   14
5. 5.

   Luz's math book asks which of four expressions is equal to 7^10. The page has a doodle of a rocket. Which expression is equal to 7^10?

   • 7^2 × 7^5
   • 7^4 × 7^6
   • (7^7)^3
   • 7^20 ÷ 7^2
6. 6.

   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
7. 7.

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

   Jun's worksheet asks about (3 × 5)^2 and gives four choices. Every choice looks friendly. Which expression is equal to (3 × 5)^2?

   • 3 × 5^2
   • 15 × 2
   • 3^2 × 5
   • 3^2 × 5^2
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