Chapter 7.3, Problem 4CYU

To determine

To write the expression in exponential form.

Answer to Problem 4CYU

  ${(8n)}^{\frac{1}{2}}$

Explanation of Solution

Given:

Expression: $\sqrt{8n}$

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 $\sqrt{8n}$ ,

Applying the formula,

  $\sqrt{8n}=\sqrt{{(8n)}^1}$

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

Hence, applying the above formula,

  $\sqrt{{(8n)}^1}={(8n)}^{\frac{1}{2}}$

Conclusion:

Therefore, the exponential form of the expression is ${(8n)}^{\frac{1}{2}}.$