Q. 124 - Intermediate Algebra

Question

In the following exercises, write with a rational exponent. 

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

Step-by-Step Solution

Answer

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

Part (b). $\sqrt[10]{s}=s^{\frac{1}{10}}$

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

Part (a) Step 1. Rational exponent of r 8

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 s 10

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 t 4

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

The index is $4$

The denominator of the exponent will be $4$

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