standard_description: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^(3) = 5(^(1/3))^(3) to hold, so (5^(1/3))^(3) must equal 5.
problem_activity: Problem 1
Jack mixes yellow and blue paint to make a green paint that he will use to paint his basement. He uses a ratio of 3 pints of yellow paint for every 2 pints of blue paint. Jack pours 18 pints of yellow paint into a bucket.
a.   How many pints of blue paint should Jack add to the bucket?
b.   Jack's friend Kyle wants to help paint. Kyle said he has a green paint that is 9 parts yellow paint to 4 parts blue paint. Is Kyle's paint the same shade green as Jack's? Explain why or why not.
Problem 2
Terrance bikes 3.6 miles to school in 18 minutes. Jacqueline bikes 5.4 miles to school in 30 minutes. Assuming each student rode at a constant speed, who is traveling at a faster speed?
Problem 3
At the corner market, you can buy rice by the pound. The table below shows some weights and their corresponding costs.
| **           Rice (lbs.)          ** | **           Cost ($)          ** |
|--------------------------------------|-----------------------------------|
|                  2                   |                11                 |
|                  10                  |                55                 |
|                  13                  |                 ?                 |
|                  ?                   |                88                 |
a.   How much does 13 pounds of rice cost?
b.   How many pounds of rice can you buy with $88?


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