Chapter 7, Problem 29SGR

To determine

To Simplify: The expression ${625}^{\frac{1}{4}}$

Answer to Problem 29SGR

  ${625}^{\frac{1}{4}}=5$

Explanation of Solution

Given information:

The expression ${625}^{\frac{1}{4}}$

Concept and Formula Used:

Rule of exponent.

  $\sqrt[n]{a}=a^{\frac{1}{n}},{\left(ab\right)}^n=a^n{b}^n$

BODMAS rule

Calculation:

The given expression is

  $\begin{array}{l}{625}^{\frac{1}{4}}\\ {625}^{\frac{1}{4}}={\left(5\times 5\times 5\times 5\right)}^{\frac{1}{4}}\\ {625}^{\frac{1}{4}}={\left(5^4\right)}^{\frac{1}{4}}\\ \text{Using }{\left(a^m\right)}^n=a^{m\times n}\\ {625}^{\frac{1}{4}}={\left(5\right)}^{4\times \frac{1}{4}}\\ {625}^{\frac{1}{4}}={\left(5\right)}^1\\ {625}^{\frac{1}{4}}=5\end{array}$

Conclusion:

  ${625}^{\frac{1}{4}}=5$