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.

   The garden club has 2^3 packets with 2^6 bean seeds in each, planted equally in 2^5 rows. Zee hums to the seeds. Each row gets 2^? seeds. What is the missing exponent?

   4
2. 2.

   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
3. 3.

   Jun's robot shows four expressions, but only one is equal to 2^8. It hums while it waits. Which expression is equal to 2^8?

   • 2^2 × 2^4
   • (2^5)^3
   • 2^16 ÷ 2^2
   • (2^4)^2
4. 4.

   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?

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

   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
6. 6.

   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
7. 7.

   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
8. 8.

   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
9. 9.

   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?

   • 12 × 2
   • 3^2 × 4
   • 3 × 4^2
   • 3^2 × 4^2
10. 10.

    Milo's puzzle card says (-2)^3 × (-2)^2. The minus signs look very serious. How do you write (-2)^3 × (-2)^2 as a single power of (-2)?

    (-2)^5