Chapter 7.3, Problem 42PPS

To determine

To simplify ${49}^{\frac{5}{2}}.$

Answer to Problem 42PPS

  $16807$

Explanation of Solution

Given:

  ${49}^{\frac{5}{2}}$

Formula used:

  $a^{\frac{1}{n}}=\sqrt[n]{a}$

Calculation:

  $\Rightarrow {49}^{\frac{5}{2}}$

  $\Rightarrow {({49}^{\frac{1}{2}})}^5$

  $\Rightarrow {\left(\sqrt[]{49}\right)}^5$

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

  $\Rightarrow {\left(\sqrt[]{7\times 7}\right)}^5$

  $\Rightarrow {\left(\sqrt[]{7^2}\right)}^5$

  $\Rightarrow {(7)}^5$

  $\Rightarrow 16807$

Conclusion:

Therefore, the simplified form of ${49}^{\frac{5}{2}}$ is $16807$ .