Chapter 7.3, Problem 2AGP

To determine

To simplify the given expression.

Answer to Problem 2AGP

4

Explanation of Solution

Given:

Expression: $\sqrt[3]{64}$

Formula used:

  $x^{\frac{a}{b}}=\sqrt[b]{x^a}$

Calculation:

Consider the given expression $\sqrt[3]{64}$ ,

  $\sqrt[3]{64}=\sqrt[3]{{\left(64\right)}^1}$

Here, 64 can be written as $4^3.$

Applying the above formula,

  $\begin{array}{c}\sqrt[3]{64}=\sqrt[3]{{\left(4^3\right)}^1}\\ =\sqrt[3]{4^3}\\ =4^{\frac{3}{3}}\\ =4^1\\ =4\end{array}$

Conclusion:

Therefore, the simplified form of the expression is 4.