Q. 119 - Intermediate Algebra

Question

In the following exercise, write as a radical expression.

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

Step-by-Step Solution

Answer

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

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

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

Part (a) Step 1. Radical expression of x 1 2

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 y 1 3

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 z 1 4

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

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

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