Chapter 7.3, Problem 63PPS

To determine

To write the expression in exponential form.

Answer to Problem 63PPS

  ${29}^{\frac{1}{3}}$

Explanation of Solution

Given:

Expression: $\sqrt[3]{29}$

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 $\sqrt[3]{29}$ ,

  $\sqrt[3]{29}=\sqrt[3]{{29}^1}$

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

Hence, applying the above formula,

  $\sqrt[3]{{29}^1}={29}^{\frac{1}{3}}$

Conclusion:

Therefore, the exponential form of the expression is ${29}^{\frac{1}{3}}.$