Chapter 7.3, Problem 3AGP

To determine

To write the radical in exponent form or write the exponent in radical form.

Answer to Problem 3AGP

  $\sqrt[3]{27}$

Explanation of Solution

Given information:

  ${27}^{\frac{1}{3}}$

Formula used:

  $\begin{array}{l}\text{Radical rule:}\text{}\sqrt{m}=m^{\frac{1}{2}}\\ \text{Radical rule:}\text{}\sqrt[n]{m}=m^{\frac{1}{n}}\\ \text{Exponent rule:}\text{}{m}^{\frac{1}{2}}=\sqrt{m}\\ \text{Exponent rule:}\text{}{m}^{\frac{1}{n}}=\sqrt[n]{m}\end{array}$

Calculation:

The expression is in exponent form. So, it required to write this expression in radical form.

Use the rule $m^{\frac{1}{n}}=\sqrt[n]{m}$ , to write the given expression in radical form.

  ${27}^{\frac{1}{3}}=\sqrt[3]{27}$

Conclusion:

The radical form of the expression is $\sqrt[3]{27}$ .