Chapter 7.3, Problem 39PPS

To determine

To simplify ${729}^{\frac{5}{6}}.$

Answer to Problem 39PPS

  $243$

Explanation of Solution

Given:

  ${729}^{\frac{5}{6}}$

Formula used:

  $a^{\frac{1}{n}}=\sqrt[n]{a}$

Calculation:

  $\Rightarrow {729}^{\frac{5}{6}}$

  $\Rightarrow {({729}^{\frac{1}{6}})}^5$

  $\Rightarrow {\left(\sqrt[6]{729}\right)}^5$

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

  $\Rightarrow {\left(\sqrt[6]{3\times 3\times 3\times 3\times 3\times 3}\right)}^5$

  $\Rightarrow {\left(\sqrt[6]{3^6}\right)}^5$

  $\Rightarrow {(3)}^5$

  $\Rightarrow 243$

Conclusion:

Therefore, the simplified form of ${729}^{\frac{5}{6}}$ is $243$ .