Question

In the following exercises, write with a rational exponent.

$ⓐ\sqrt[7]{x}ⓑ\sqrt[9]{y}ⓒ\sqrt[5]{f}$

Short answer

Part (a). $\sqrt[7]{x}=x^{\frac{1}{7}}$

Part (b). $\sqrt[9]{y}=y^{\frac{1}{9}}$

Part (c).$\sqrt[5]{f}=f^{\frac{1}{5}}$

Step-by-step solution

Part (a) Step 1. Rational exponent of  x7 

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

The index is$7$

The denominator of the exponent will be $7$.

$\sqrt[7]{x}=x^{\frac{1}{7}}$

Part (b) Step 1. Rational exponent of  y9

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

The index is $9$

The denominator of the exponent will be $9$.

$\sqrt[9]{y}=y^{\frac{1}{9}}$

Part (c) Step 1. Rational exponent of  f5

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

The index is $5$

The denominator of the exponent will be $5$

$\sqrt[5]{f}=f^{\frac{1}{5}}$