Question

In the following exercise, write as a radical expression.

$ⓐx^{\frac{1}{2}}ⓑy^{\frac{1}{3}}ⓒz^{\frac{1}{4}}$

Short answer

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

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

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

Step-by-step solution

Part (a) Step 1. Radical expression of x12

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,

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

Part (b). Radical expression of y13

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

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

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

Part (c) Radical expression of z14

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

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

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