Chapter 7.3, Problem 95PFA

To determine

To write the expression in exponential form.

Answer to Problem 95PFA

  $16c^{\frac{5}{4}}$

Explanation of Solution

Given:

Expression: $16\sqrt[4]{c^5}$

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 expression,

  $16\sqrt[4]{c^5}$

Applying the above formula,

  $\begin{array}{c}$ 16\sqrt[4]{c^5}=16{(c^5)}^{\frac{1}{4}}$=16c^{\frac{5}{4}}\end{array}$

Conclusion:

Therefore, the exponential form of the expression is $16c^{\frac{5}{4}}.$