Question: What advantages are there in using rational exponents as opposed to radicals? Provide examples of each.

Hint: First, define rational exponents and give examples. Then, define radicals and give examples (it might also help to define the index and radicand of a radical). Finally, tell how the two concepts are related, and give examples of when you might want to use rational exponents instead of radicals.

"Real-Life" Relationship: In finance, rational exponents are often used in the calculation of compound interest. For example, if you deposit $100 in a savings account that pays 2% compound interest per year, then the equation to model the amount A you have after t years is: A = $100(1.02)t Keep in mind that in this case, t does not have to be a whole number. After 6 months, we would plug in t = 1/2 (6 months is half of a year).

Challenge: Can you find an example of uses of rational exponents in real life? For example: if we want a cubic box with volume 64 cubic inches, then each side must be 4 inches long, since 4 is the cube root of 64. That is, 641/3 = 4.