Skip main navigation

# Rational powers in practice

Solving exercises about basic properties of rational powers.

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}.]

This article is from the free online

Created by

## Reach your personal and professional goals

Unlock access to hundreds of expert online courses and degrees from top universities and educators to gain accredited qualifications and professional CV-building certificates.

Join over 18 million learners to launch, switch or build upon your career, all at your own pace, across a wide range of topic areas.

Start Learning now