$a)4^{-\frac{3}{2}}=\frac{1}{4^{\frac{3}{2}}}=\frac{1}{\sqrt{4^3}}=\frac{1}{{\left(\sqrt{4}\right)}^3}=\frac{1}{2^3}=\frac{1}{8}$

$b){81}^{1,5}={81}^{1\frac{1}{2}}={81}^{\frac{3}{2}}=\sqrt{{81}^3}={\left(\sqrt{81}\right)}^3=9^3=729$

$c){\left(\frac{1}{81}\right)}^{-\frac{3}{4}}={81}^{\frac{3}{4}}=\sqrt[4]{{81}^3}={\left(\sqrt[4]{81}\right)}^3=3^3=27$

$d){\left(\frac{1}{4}\right)}^{-2,5}=4^{2,5}=4^{2\frac{1}{2}}=4^{\frac{5}{2}}=\sqrt{4^5}={\left(\sqrt{4}\right)}^5=2^5=32$