Chapter 7.3, Problem 26PPS

To determine

To simplify the given expression.

Answer to Problem 26PPS

4

Explanation of Solution

Given:

Expression: $\sqrt[5]{1024}$

Formula used:

  $x^{\frac{a}{b}}=\sqrt[b]{x^a}$

Calculation:

Consider the given expression $\sqrt[5]{1024}$ ,

  $\sqrt[5]{1024}=\sqrt[5]{{\left(1024\right)}^1}$

Here, 1024 can be written as $4^5.$

Applying the above formula,

  $\begin{array}{c}\sqrt[5]{1024}=\sqrt[5]{{(4^5)}^1}\\ =\sqrt[5]{4^5}\\ =4^{\frac{5}{5}}\\ =4\end{array}$

Conclusion:

Therefore, the simplified form of the expression is 4.