Question

In the following exercises, write with a rational exponent.

$ⓐ\sqrt[8]{r}ⓑ\sqrt[10]{s}ⓒ\sqrt[4]{t}$

Short answer

Part (a). $\sqrt[8]{r}=r^{\frac{1}{8}}$

Part (b). role="math" localid="1644748622060" $\sqrt[10]{s}=s^{\frac{1}{10}}$

Part (c).$\sqrt[4]{t}=t^{\frac{1}{4}}$

Step-by-step solution

Part (a) Step 1. Rational exponent of  r8

We know that,$\sqrt[n]{a}=a^{\frac{1}{n}}$

The index is $8$

The denominator of the exponent will be $8$.

$\sqrt[8]{r}=r^{\frac{1}{8}}$

Part (b) Step 1. Rational exponent of  s10

We know that,$\sqrt[n]{a}=a^{\frac{1}{n}}$

The index is $10$

The denominator of the exponent will be $10$

$\sqrt[10]{s}=s^{\frac{1}{10}}$

Part (c) Step 1. Rational exponent of  t4

We know that, $\sqrt[n]{a}=a^{\frac{1}{n}}$

The index is$4$

The denominator of the exponent will be$4$

4$\sqrt[4]{t}=t^{\frac{1}{4}}$