<s>[INST] Exponential Equations with Fractions I have had some issues with the following two equations:

$$ \frac{3^{n-2}}{9^{1-n}}=9$$
  $$\frac{5^{3n-3}}{25^{n-3}}=125$$

If anyone could work them out step by step that would be awesome. I keep arriving at the wrong answer and believe it could be related to the addition of exponents towards the end of the question.
note:$n$ is different in each equation.
 [/INST] $\frac{3^{n-2}}{9^{1-n}}=9$
$\implies\frac{3^{n-2}}{3^{2(1-n)}}=9$
$\implies\frac{3^{n-2}}{3^{2-2n}}=9$ 
$\implies3^{(n-2)-(2-2n)}=3^{2} [a^{(m-n)}=\frac{a^m}{b^m}]$
$\implies3^{3n-4}=3^2$
$\implies{3n-4}=2$ 
$\implies n=2$ 
$\frac{5^{3n-3}}{25^{n-3}}$
$=\frac{5^{6-2}}{25^{2-3}} [put(n=2)]$
$=\frac{5^4}{5^{-1}}$
$=5^{4-1}$
$=5^3=125$
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