<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] $$ \frac {36^{2n}.6^{n+2}} {216^{n+2}}=\frac {(6^2)^{2n}.6^{n+2}} {(6^3)^{n+2}}=\frac{6^{2\cdot2n+(n+2)}}{6^{3\cdot(n+2)}}=\frac{6^{5n+2}}{6^{3n+6}}=6^{(5n+2)-(3n+6)}=6^{2n-4}$$
</s>