Question

simplify ( 81 divided by 16 ) raise to the power -3 upon 4 multiply by ( 25 divided by 9 ) raise to the power -3 upon 2

Answer 1

$$\begin{gathered} {\left(\frac{81}{16}\right)}^{-\frac{3}{4}}\times {\left(\frac{25}{9}\right)}^{-\frac{3}{2}} \\ ={\left(\frac{16}{81}\right)}^{\frac{3}{4}}\times {\left(\frac{9}{25}\right)}^{\frac{3}{2}}\left[\mathrm{as},a^{-m}={\left(\frac{1}{a}\right)}^m\right] \\ ={\left(\frac{2\times 2\times 2\times 2}{3\times 3\times 3\times 3}\right)}^{\frac{3}{4}}\times {\left(\frac{3\times 3}{5\times 5}\right)}^{\frac{3}{2}} \\ ={\left[{\left(\frac{2}{3}\right)}^4\right]}^{\frac{3}{4}}\times {\left[{\left(\frac{3}{5}\right)}^2\right]}^{\frac{3}{2}} \\ ={\left(\frac{2}{3}\right)}^{4\times \frac{3}{4}}\times {\left(\frac{3}{5}\right)}^{2\times \frac{3}{2}} \\ ={\left(\frac{2}{3}\right)}^3\times {\left(\frac{3}{5}\right)}^3 \\ =\frac{8}{27}\times \frac{27}{125} \\ =\frac{8}{125} \end{gathered}$$