Question
\[
3^{x-1}=9,\quad 4^{y+2}=64
\]
Solution
\[
9=3^2 \Rightarrow 3^{x-1}=3^2
\]
\[
x-1=2 \Rightarrow x=3
\]
\[
64=4^3 \Rightarrow 4^{y+2}=4^3
\]
\[
y+2=3 \Rightarrow y=1
\]
\[
\frac{x}{y}=\frac{3}{1}=3
\]
Answer
\[
\boxed{3}
\]