Question

evaluate
(9/4)^-3/2_*(125/27)^-2/3_* (3/5)^-3
divided by (root of 2)⁴

Answer 1

$$\begin{gathered} \frac{{\left({\displaystyle \frac{9}{4}}\right)}^{-3/2}\times {\left({\displaystyle \frac{125}{27}}\right)}^{-2/3}\times {\left({\displaystyle \frac{3}{5}}\right)}^{-3}}{{\left(\sqrt{2}\right)}^4} \\ =\frac{{\left[{\left({\displaystyle \frac{3}{2}}\right)}^2\right]}^{-3/2}\times {\left[{\left({\displaystyle \frac{5}{3}}\right)}^3\right]}^{-2/3}\times {\left({\displaystyle \frac{3}{5}}\right)}^{-3}}{4} \\ =\frac{{\left({\displaystyle \frac{3}{2}}\right)}^{-3}\times {\left({\displaystyle \frac{5}{3}}\right)}^{-2}\times {\left({\displaystyle \frac{3}{5}}\right)}^{-3}}{4} \\ =\left[{\left(\frac{2}{3}\right)}^3\times {\left(\frac{3}{5}\right)}^2\times {\left(\frac{5}{3}\right)}^3\right]÷4 \\ =\left[\frac{8}{27}\times \frac{9}{25}\times \frac{125}{27}\right]\times \frac{1}{4} \\ =\frac{10}{81} \end{gathered}$$