Chapter 7.3, Problem 43PPS

To determine

To simplify ${\left(\frac{9}{100}\right)}^{\frac{3}{2}}.$

Answer to Problem 43PPS

  $\frac{27}{1000}$

Explanation of Solution

Given:

  ${\left(\frac{9}{100}\right)}^{\frac{3}{2}}$

Formula used:

  $a^{\frac{1}{n}}=\sqrt[n]{a}$

Calculation:

  $\Rightarrow {\left(\frac{9}{100}\right)}^{\frac{3}{2}}$

  $\Rightarrow {\left[{\left(\frac{9}{100}\right)}^{\frac{1}{2}}\right]}^3$

  $\Rightarrow {\left(\sqrt[]{\frac{9}{100}}\right)}^3$

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

  $\Rightarrow {\left(\sqrt[]{\frac{3\times 3}{10\times 10}}\right)}^3$

  $\Rightarrow {\left(\sqrt[]{{\left(\frac{3}{10}\right)}^2}\right)}^3$

  $\Rightarrow {\left(\frac{3}{10}\right)}^3$

  $\Rightarrow \frac{27}{1000}$

Conclusion:

Therefore, the simplified form of ${\left(\frac{9}{100}\right)}^{\frac{3}{2}}$ is $\frac{27}{1000}$ .