[tex]\displaystyle\bf\\{\bf d)}~\left\{\left[\left(\frac{2}{3}\right)^2\right]^3\right\}^4=\left(\frac{2}{3}\right)^{2\times3\times4}=\boxed{\bf\left(\frac{2}{3}\right)^{24}}=\boxed{\bf\frac{2^{24}}{3^{24}}}\\\\\\\\{\bf e)}~\left[\left(\frac{3}{5}\right)^{-7}\right]^5=\left[\left(\frac{5}{3}\right)^7\right]^5=\left(\frac{5}{3}\right)^{7\times5}=\boxed{\bf\left(\frac{5}{3}\right)^{35}}=\boxed{\bf\frac{5^{35}}{3^{35}}}[/tex]
