Chapter 11, Problem 28CCSR

To determine

Rewrite the expression $\sqrt[4]{81x^3}$ using rational exponents.

Answer to Problem 28CCSR

  $\sqrt[4]{81x^3}=3·\sqrt[4]{x^3}$

Explanation of Solution

Given:

The expression: $\sqrt[4]{81x^3}$

Concept Used:

Use the rule: $\sqrt[n]{x^n}=x^{n·\frac{1}{n}}=x$

Calculation:

  $\sqrt[4]{81x^3}=\sqrt[4]{81}·\sqrt[4]{x^3}=\sqrt[4]{3^4}·\sqrt[4]{x^3}=3^{4·\frac{1}{4}}·\sqrt[4]{x^3}=3·\sqrt[4]{x^3}$

Thus, $\sqrt[4]{81x^3}=3·\sqrt[4]{x^3}$