Chapter 7.3, Problem 22PPS

To determine

To write the expression in exponential form.

Answer to Problem 22PPS

  ${44}^{\frac{1}{2}}$

Explanation of Solution

Given:

Expression: $\sqrt{44}$

Formula used:

A relationship between radical and exponential is:

  $x^{\frac{a}{b}}=\sqrt[b]{x^a}$

Here, $x^{\frac{a}{b}}$ is an exponential whereas $\sqrt[b]{x^a}$ is a radical.

Calculation:

Consider the given expression $\sqrt{44}$ ,

The above expression is of the form $\sqrt[b]{x^a}.$

Applying the above formula,

  $\begin{array}{c}\sqrt{44}=\sqrt{{44}^1}\\ ={44}^{\frac{1}{2}}\end{array}$

Conclusion:

Therefore, the exponential form of the expression is

  ${44}^{\frac{1}{2}}.$