Question

In the following exercises, write with a rational exponent.

$\sqrt[3]{7c}ⓑ\sqrt[7]{12d}ⓒ2\sqrt[4]{6b}$

Short answer

Part (a). $\sqrt[3]{7c}={\left(7c\right)}^{\frac{1}{3}}$

Part (b). $\sqrt[7]{12d}={\left(12d\right)}^{\frac{1}{7}}$

Part (c).$2\sqrt[4]{6b}=2{\left(6b\right)}^{\frac{1}{4}}$

Step-by-step solution

Part (a) Step 1. Rational exponent of  73

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

The index is $3$

The denominator of the exponent will be $3$.

$\sqrt[3]{7c}={\left(7c\right)}^{\frac{1}{3}}$

Part (b) Step 1. Rational exponent of  12d7

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

The index is$7$

The denominator of the exponent will be $7$

$\sqrt[7]{12d}={\left(12d\right)}^{\frac{1}{7}}$

Part (c) Step 1. Rational exponent of  26b5

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

The index is$5$

The denominator of the exponent will be $5$.

$2\sqrt[4]{6b}=2{\left(6b\right)}^{\frac{1}{4}}$