Question

All changes saved1. (02.02 MC)Describe how to transform (827)into an expression with a rational exponent. Make sure you respond with complete sentences. (10 points)

Answer 1

We want write this as a rational exponent

`(\sqrt[5]{x^7})^3`

This simply means the 5th root of x to power 7 all raised to power 5.

First step is to write the root form to exponent form we have

`\begin{gathered} \sqrt[5]{x^7}=(x^7)^{(1)/(5)^{}} \\ =(x^7)^{*(1)/(5)^{}} \\ x^{(7)/(5)} \end{gathered}`

Next is the exponent 3, we have

`\begin{gathered} (x^{(7)/(5)})^3 \\ (x^{(7)/(5)})^(*3) \\ x^{(21)/(5)} \end{gathered}`

Hence the answer is

`x^{(21)/(5)}`