Q. 121 - Intermediate Algebra

Question

In the following exercises, write as a radical expression.  

$ⓐ u^{\frac{1}{5}} ⓑ v^{\frac{1}{9}} ⓒ w^{\frac{1}{20}}$

Step-by-Step Solution

Answer

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

part (b). $v^{\frac{1}{9}}=\sqrt[9]{v}$

Part (c). $w^{\frac{1}{20}}=\sqrt[20]{w}$

Part (a) Step 1. Radical expression of u 1 5

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

The denominator of the rational exponent is $5$, so the index of the radical is $5$. We do not show the

index when it is $5$.

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

Part (b). Radical expression of v 1 9

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

The denominator of the exponent is $9$, so the index is $9$.

$v^{\frac{1}{9}}=\sqrt[9]{v}$

Part (c) Radical expression of w 1 20

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

The denominator of the exponent is $20$, so the index is $20$.

$w^{\frac{1}{20}}=\sqrt[20]{w}$