Chapter 7.3, Problem 38PPS

To determine

To simplify ${625}^{\frac{3}{4}}.$

Answer to Problem 38PPS

  $125$

Explanation of Solution

Given:

  ${625}^{\frac{3}{4}}$

Formula used:

  $a^{\frac{1}{n}}=\sqrt[n]{a}$

Calculation:

  $\Rightarrow {625}^{\frac{3}{4}}$

  $\Rightarrow {({625}^{\frac{1}{4}})}^3$

  $\Rightarrow {\left(\sqrt[4]{625}\right)}^3$

  $[\because a^{\frac{1}{n}}=\sqrt[n]{a}]$

  $\Rightarrow {\left(\sqrt[4]{5\times 5\times 5\times 5}\right)}^3$

  $\Rightarrow {\left(\sqrt[4]{5^4}\right)}^3$

  $\Rightarrow {(5)}^3$

  $\Rightarrow 125$

Conclusion:

Therefore, the simplified form of ${625}^{\frac{3}{4}}$ is $125$ .