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.

   Kira's puzzle card has four expressions. Only one is equal to 3^9, and it wins a star. Which expression is equal to 3^9?

   • 3^3 × 3^3
   • 3^12 ÷ 3^3
   • (3^4)^5
   • 3^18 ÷ 3^2
4. 4.

   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
5. 5.

   Pia shares 2^4 crayons equally among 2^4 classmates, so each gets 2^4 ÷ 2^4 = 2^0 crayons. Nobody fights over colors. How many crayons does each classmate get?

   1
6. 6.

   Ren's bouncy ball reaches 2/3 of its last height on every bounce. After 1 bounce and then 2 more, it reaches (2/3)^1 × (2/3)^2 of its first height. What fraction is that?

   8/27
7. 7.

   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
8. 8.

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

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