Chapter 7.3, Problem 65PPS

To determine

To write the expression in exponential form.

Answer to Problem 65PPS

  $2(a^{\frac{1}{3}})$

Explanation of Solution

Given:

Expression: $2\sqrt[3]{a}$

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 $2\sqrt[3]{a}$ ,

  $2\sqrt[3]{a}=2\sqrt[3]{a^1}$

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

Hence, applying the above formula,

  $2\sqrt[3]{a^1}=2(a^{\frac{1}{3}})$

Conclusion:

Therefore, the exponential form of the expression is $2(a^{\frac{1}{3}}).$