Question

In the following exercises, write as a radical expression.

$ⓐr^{\frac{1}{2}}ⓑs^{\frac{1}{3}}ⓒt^{\frac{1}{4}}$

Short answer

Part (a). $r^{\frac{1}{2}}=\sqrt{r}$

Part (b). $s^{\frac{1}{3}}=\sqrt[3]{s}$

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

Step-by-step solution

Part (a) Step 1. Radical expression of  r12

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

The denominator of the rational exponent is $2$, so the index of the radical is $2$. We do not show the index when it is $2$.

So,

$r^{\frac{1}{2}}=\sqrt{r}$

Part (b). Radical expression of s13

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

The denominator of the exponent is $3$, so the index is $3$.

$s^{\frac{1}{3}}=\sqrt[3]{s}$

Part (c) Radical expression of t14

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

The denominator of the exponent is $4$, so the index is $4$.

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