[tex]a)\\\\\frac{125*15}{3^3*5^4}=\frac{5^3*3*5}{3^3*5^4}=\frac{5^4*3}{3^3*5^4}=\frac{1}{3^2}=\frac19[/tex]
[tex]b)\\\\\frac{(3^5)^4*6^4}{9^7*4^2}=\frac{3^{20}*3^4*2^4}{(3^2)^7*(2^2)^2}=\frac{3^{24}*2^4}{3^{14}*2^4}=3^{10}[/tex]
[tex]c)\\\\\frac{9^4*4^4}{6^{10}}=\frac{(3^2)^4*(2^2)^4}{6^{10}}=\frac{3^8*2^8}{6^{10}}=\frac{6^8}{6^{10}}=\frac{1}{6^2}=\frac1{36}[/tex]
[tex]d)\\\\\frac{0.25^3:0.5^3}{5^3}=\frac{(\frac{0.25}{0.5})^3}{5^3}=(\frac{0.5}{5})^3=0.1^3=0.001[/tex]
