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.

   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.

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

   14
4. 4.

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

   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?

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

   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.

   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 × 5^3
   • 2^3 × 5
   • 2^3 × 5^3
   • 10 × 3
9. 9.

   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
10. 10.

    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