Name
Exponents – Product Rule
September 10, 2019
Instructions: Attempt all problems. For Section 1: Simplifying, please simplify each expression using the extended form before
fully simplifying. For Section 2: Application, you may choose the extended form or use the Product Rule to simplify the
expression.
Section 1: Simplifying
1. 𝑤 4 ∙ 𝑤 5
2. 𝑘 8 ∙ 𝑘 2 ∙ 𝑘
3. 𝑛7 ∙ 𝑛6
4. 5𝑎2 ∙ 6𝑎2
5. 3𝑐 3 ∙ −2𝑐 5
6. 6𝑝4 ∙ 4𝑝4
7. 𝑎2 𝑏 4 𝑐 3 ∙ 𝑎 𝑏 3 𝑐
8. 10𝑥 6 𝑦 4 ∙ −10𝑥 4
9. −2𝑣 10 ∙ −3𝑐 5
Name
Exponents – Product Rule
September 10, 2019
Section 2: Application Leave all answers as an exponential expression.
10. The length of a rectangle is given by the expression 6𝑥 3 and its width is 8𝑥 4 . Find the area of the rectangle.
11. The length of a rectangle is represented by the expression 4𝑚4 and its width as 3𝑚5 . Find the area of the rectangle.
12. The side of a square can be expressed as 5𝑥 3 𝑦 4 . Find the area of the square.
13. A rocket travels at a speed 24 miles per hour, how long will the rocket travel in 22 hours?
14. There are
section of land?
blades of grass in each acre of land, and a section of land spans
acres wide. How much total grass is in the
15. The average human eye can detect 76 different colors. How many total colors would 32 human eyes detect?