Q. 125 - Intermediate Algebra

Question

In the following exercises, write with a rational exponent.  

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

Step-by-Step Solution

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

Part (a) Step 1. Rational exponent of 7 3

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 12 d 7

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 2 6 b 5

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

The index is $5$

The denominator of the exponent will be $5$.

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