Chapter 7.3, Problem 3BGP

To determine

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

Answer to Problem 3BGP

  $\sqrt[4]{256}$

Explanation of Solution

Given information:

  ${256}^{\frac{1}{4}}$

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.

  ${256}^{\frac{1}{4}}=\sqrt[4]{256}$

Conclusion:

The radical form of the expression is $\sqrt[4]{256}$ .