解：$(2)$因为$(\frac {5}{4})^3=\frac {5}{4}×\frac {5}{4}×\frac {5}{4}=\frac {125}{64}，$
$(\frac {4}{5})^{-3}=\frac {1}{(\frac {4}{5})^3}=\frac {1}{\frac {4}{5}×\frac {4}{5}×\frac {4}{5}}=\frac {5}{4}×\frac {5}{4}×\frac {5}{4}=\frac {125}{64}，$
所以$(\frac {5}{4})^3=(\frac {4}{5})^{-3}。$
$(4)①(\frac {3}{8})^{-4}=(\frac {8}{3})^4，$
所以原式$=(\frac {8}{3})^4×(\frac {3}{4})^4=(\frac {8}{3}×\frac {3}{4})^4=2^4=16；$
$ ②(-\frac {1}{2})^{-3}×2^{-4}-4^{-2}×(-0.25)^{-3}$
$=(-2)^3×(\frac {1}{2})^4-(\frac {1}{4})^2×(-4)^3$
$ =[(-2)×\frac {1}{2}]^3×\frac {1}{2}-[\frac {1}{4}×(-4)]^2×(-4)$
$ =-\frac {1}{2}-(-4)$
$ =-\frac {1}{2}+4$
$ =3\frac {1}{2}$
