Q. 126 - Intermediate Algebra

Question

In the following exercises, write with a rational exponent.   

$ⓐ \sqrt[4]{5x} ⓑ \sqrt[8]{9y} ⓒ 7\sqrt[5]{3z}$

Step-by-Step Solution

Answer

Part (a). $\sqrt[4]{5x}={\left(5x\right)}^{\frac{1}{4}}$

Part (b). $\sqrt[8]{9y}={\left(9y\right)}^{\frac{1}{8}}$

Part (c). $7\sqrt[5]{3z}=7{\left(3z\right)}^{\frac{1}{5}}$

Part (a) Step 1. Rational exponent of 5 x 4

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

The index is $4$

The denominator of the exponent will be $4$.

$\sqrt[4]{5x}={\left(5x\right)}^{\frac{1}{4}}$

Part (b) Step 1. Rational exponent of 9 y 8

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

The index is $8$

The denominator of the exponent will be $8$.

$\sqrt[8]{9y}={\left(9y\right)}^{\frac{1}{8}}$

Part (c) Step 1. Rational exponent of 7 3 z 5

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

The index is $5$

The denominator of the exponent will be $5$

$7\sqrt[5]{3z}=7{\left(3z\right)}^{\frac{1}{5}}$