Q. 122 - Intermediate Algebra

Question

In the following exercises, write as a radical expression.   

$ⓐ g^{\frac{1}{7}}ⓑ h^{\frac{1}{5}} ⓒ j^{\frac{1}{25}}$

Step-by-Step Solution

Answer

Part (a). $g^{\frac{1}{7}}=\sqrt[7]{g}$

Part (b). $h^{\frac{1}{5}}=\sqrt[5]{h}$

Part (c). $j^{\frac{1}{25}}=\sqrt[25]{j}$

Part (a) Step 1. Radical expression of g 1 7

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

The denominator of the rational exponent is $7$, so the index of the radical is $7$. We do not show the

index when it is $7$.

$g^{\frac{1}{7}}=\sqrt[7]{g}$

Part (b). Radical expression of h 1 5

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

The denominator of the exponent is $5$, so the index is $5$.

$h^{\frac{1}{5}}=\sqrt[5]{h}$

Part (c) Radical expression of j 1 25

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

The denominator of the exponent is $25$, so the index is $25$.

$j^{\frac{1}{25}}=\sqrt[25]{j}$