Q. 8.52 - Intermediate Algebra

Question

Write as a radical expression:

(a) $b^{\frac{1}{6}}$

(b) $z^{\frac{1}{5}}$

(c) $p^{\frac{1}{4}}$

Step-by-Step Solution

Answer

The radical expression of $b^{\frac{1}{6}}$ is $\sqrt[6]{b}$.

The radical expression of $z^{\frac{1}{5}}$ is $\sqrt[5]{z}$.

The radical expression of $p^{\frac{1}{4}}$ is $\sqrt[4]{p}$.

Part (a) Step 1. Given

The expression $b^{\frac{1}{6}}$

To write the given expression in the form of $\sqrt[n]{a}$

Part (a) Step 2. Write as rational expression

The denominator of rational exponent is $6$, so the index of the radical is $6$.

The radical expression is $\sqrt[6]{b}$

Part (b) Step 1. Given

The expression $z^{\frac{1}{5}}$

To write the given expression in the form of $\sqrt[n]{a}$

Part (b) Step 2. Write as rational expression

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

The radical expression is $\sqrt[5]{z}$

Part (c) Step 1. Given

The expression $p^{\frac{1}{4}}$

To write the given expression in the form of $\sqrt[n]{a}$

Part (c) Step 2. Write as rational expression

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

The radical expression is $\sqrt[4]{p}$