<s>[INST] Simplifying expressions with algebraic indices I am having a ridiculous amount of trouble solving questions of this style - this one in particular, I know the answer is $6^{2n-4}$ but I can't get there!!!! 
$ \frac {36^{2n}.6^{n+2}} {216^{n+2}}$
Could someone please help me out with some steps involved? I would be extremely grateful! 
I understand the rules $a^x b^x = (ab)^x $ and $x^a x^b = x^{a+b} $ I just don't understand why I'm not able to get this.
These are my steps I have been taking:
$\frac {3^{2n}.12^{2n}.2^{n+2}.3^{n+2}} {12^{n+2}.18^{n+2}}$
$ \frac {3^{2n}.3^{2n}.4^{2n}.2^{n+2}.3^{n+2}} {4^{n+2}.3^{n+2}.3^{n+2}.3^{n+2}.2^{n+2}} $
I've simplified in this manner and then have tried cancelling and am coming out with completely wrong answers every time. 
 [/INST] $$\frac {36^{2n}\cdot6^{n+2}} {216^{n+2}} \equiv \frac{(6^2)^{2n} \cdot 6^{n+2}}{(6^3)^{n+2}} \equiv \frac{6^{2(2n)} \cdot 6^{n+2}}{6^{3(n+2)}} \equiv \frac{6^{4n} \cdot 6^{n+2}}{6^{3n+6}} $$ $$\equiv \frac{6^{4n+n+2}}{6^{3n+6}} \equiv \frac{6^{5n+2}}{6^{3n+6}} \equiv 6^{(5n+2)-(3n+6)} \equiv \color{green}{6^{2n-4}} \equiv 6^{2(n-2)} \equiv (6^2)^{n-2}$$
$$\equiv \;\bbox[3pt,color:black;border-radius:4px;box-shadow:2px 2px 4px green]{36^{n-2}}\;$$
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