Chapter 7.3, Problem 25PPS

To determine

To simplify the given expression.

Answer to Problem 25PPS

2

Explanation of Solution

Given:

Expression: $\sqrt[3]{8}$

Formula used:

  $x^{\frac{a}{b}}=\sqrt[b]{x^a}$

Calculation:

Consider the given expression $\sqrt[3]{8}$ ,

  $\sqrt[3]{8}=\sqrt[3]{{(8)}^1}$

Here, 8 can be written as $2^3.$

Applying the above formula,

  $\begin{array}{c}\sqrt[3]{8}=\sqrt[3]{{(2^3)}^1}\\ =\sqrt[3]{2^3}\\ =2^{\frac{3}{3}}\\ =2\end{array}$

Conclusion:

Therefore, the simplified form of the expression is 2.