Q. 123 - Intermediate Algebra

Question

In the following exercises, write with a rational exponent.

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

Step-by-Step Solution

Answer

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

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

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

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

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

The index is $7$

The denominator of the exponent will be $7$.

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

Part (b) Step 1. Rational exponent of y 9

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 f 5

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

The index is $5$

The denominator of the exponent will be $5$

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