\(a,125^5:25^3=\left(5^3\right)^5:\left(5^2\right)^3=5^{15-6}=5^9\)
\(b,27^6:9^3=\left(3^3\right)^6:\left(3^2\right)^3=3^{18-6}=3^{12}\)
\(c,4^{20}:2^{15}=\left(2^2\right)^{20}:2^{15}=2^{40-15}=2^{25}\)
\(d,24^n:2^{2n}=4^n.6^n:4^n=6^n\)
\(e,64^4.16^5:4^{20}=\left(2^6\right)^4.\left(2^4\right)^5:\left(2^2\right)^{20}=2^{24+20-40}=2^4=16\)