Rational powers in practice

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Simplify the following expressions: [a) 2^2cdot 2^{-frac{1}{2}},quad b) frac{3^3-5^2}{2^5cdot 2^{-3}},quad c) frac{(2^3)^{(2^3)}}{(2^{(3^2)})^3}.]

Exercise 2.

Let (ygeq xgeq0) and (ynot=0). Compare the quantities [2x^{frac{3}{5}}quadtext{and} quad yleft(y^{-frac{2}{5}}+y^{-frac{3}{5}}sqrt[5]{y}right).]

Exercise 3. [Solved only in the PDF file]

Compare the quantities [left(frac{1}{7}right)^{frac{1}{5}}quadtext{and}quad sqrt[5]{left(frac{1}{7}right)^4}.]