Q. 127 - Intermediate Algebra

Question

In the following exercises, write with a rational exponent.

$ⓐ \sqrt{21p} ⓑ \sqrt[4]{48q} ⓒ 4\sqrt[6]{36r}$

Step-by-Step Solution

Answer

Part (a). $\sqrt{21p}={\left(21\right)}^{\frac{1}{2}}$

Part (b). $\sqrt[4]{8q}={\left(8q\right)}^{\frac{1}{4}}$

Part (c). $4\sqrt[6]{36r}=4{\left(36r\right)}^{\frac{1}{6}}$

Part (a) Step 1. Rational exponent of 21 p

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

The index is $2$

The denominator of the exponent will be $2$.

$\sqrt{21p}={\left(21\right)}^{\frac{1}{2}}$

Part (b) Step 1. Rational exponent of 8 q 4

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

The index is $4$

The denominator of the exponent will be $4$.

$\sqrt[4]{8q}={\left(8q\right)}^{\frac{1}{4}}$

Part (c) Step 1. Rational exponent of 4 36 r 6

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

The index is $6$

The denominator of the exponent will be $6$

$4\sqrt[6]{36r}=4{\left(36r\right)}^{\frac{1}{6}}$