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.

   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.

   Esme's worksheet lists four expressions. Exactly one of them is equal to 5^6. The others are sneaky. Which expression is equal to 5^6?

   • 5^12 ÷ 5^2
   • 5^2 × 5^3
   • (5^3)^3
   • 5^2 × 5^4
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?

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

   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
7. 7.

   Zee's math book asks for the value of (3/4)^1 × (3/4)^2. The page smells like new paper. What fraction is (3/4)^1 × (3/4)^2?

   27/64
8. 8.

   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?

   • 2^3 × 5^3
   • 10 × 3
   • 2^3 × 5
   • 2 × 5^3
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?

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