jmc

Substituting the given values, we need to calculate, ${\left(\frac{3}{5}\right)}^2{\left(\frac{2}{3}\right)}^{-3}$. Because $n^{ab}={\left(n^a\right)}^b$, this expression is equivalent to $${\left(\frac{3}{5}\right)}^2{\left({\left(\frac{2}{3}\right)}^{-1}\right)}^3={\left(\frac{3}{5}\right)}^2{\left(\frac{3}{2}\right)}^3.$$Because ${\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n}$, we can rewrite this as $$\frac{3^2}{5^2}\cdot \frac{3^3}{2^3}=\frac{3^2\cdot 3^3}{5^2\cdot 2^3}.$$We then have $$\frac{3^2\cdot 3^3}{5^2\cdot 2^3}=\frac{9\cdot 27}{25\cdot 8}=\boxed{\frac{243}{200}}.$$