Solving Equation with Indices – Same Base

(i) Given that $\frac{2^{x-3}}{8^{2 y-3}}=16^{x-y}$, show that $3 x+2 y=6$.
(ii) Given also that $\frac{5^{y}}{125^{x-2}}=25$, find the value of $x$ and of $y$.

Answer