Chapter 7.3, Problem 28PPS

To determine

To simplify the given expression.

Answer to Problem 28PPS

10

Explanation of Solution

Given:

Expression: $\sqrt[4]{10,000}$

Formula used:

  $x^{\frac{a}{b}}=\sqrt[b]{x^a}$

Calculation:

Consider the given expression $\sqrt[4]{10,000}$ ,

  $\sqrt[4]{10,000}=\sqrt[4]{{\left(10,000\right)}^1}$

Here, 10000 can be written as ${10}^4.$

Applying the above formula,

  $\begin{array}{c}\sqrt[4]{10,000}=\sqrt[4]{{\left(10,000\right)}^1}\\ =\sqrt[4]{{\left({10}^4\right)}^1}\\ =\sqrt[4]{{10}^4}\\ ={10}^{\frac{4}{4}}\\ ={10}^1\\ =10\end{array}$

Conclusion:

Therefore, the simplified form of the expression is 10.