a)
\frac{5*900}{3^4*25^2}=\frac{5*30^2}{3^4*(5^2)^2}=\frac{5*(6*5)^2}{3^4*5^4}=\frac{5*6^2*5^2}{3^4*5^4}=\frac{(2*3)^2*5^3}{3^4*5^4}=
\frac{2^2*3^2*5^3}{3^4*5^4}=\frac{2^2}{3^2*5}=\frac{4}{45}
b)
\frac{2^8*5^7}{100}=\frac{2^8*5^7}{10^2}=\frac{2^8*5^7}{(2*5)^2}=\frac{2^8*5^7}{2^2*5^2}=2^6*5^5=2*10^5=200000
c)
\frac{15^4}{5^3*3^6}=\frac{(3*5)^4}{5^3*3^6}=\frac{3^4*5^4}{5^3*3^6}=\frac{5}{3^2}=\frac{5}{9}