Chapter 7.3, Problem 4AGP

To determine

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

Answer to Problem 4AGP

  $\sqrt[3]{729}$

Explanation of Solution

Given information:

  ${27}^{\frac{2}{3}}$

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.

  $\begin{array}{c}{27}^{\frac{2}{3}}={\left({27}^2\right)}^{\frac{1}{3}}\\ ={\left(729\right)}^{\frac{1}{3}}\\ =\sqrt[3]{729}\end{array}$

Conclusion:

The radical form of the expression is $\sqrt[3]{729}$ .