If $\frac{6^6+6^6+6^6+6^6+6^6+6^6}{3^6+3^6+3^6}÷\frac{4^6+4^6+4^6+4^6}{2^6+2^6}=2^n$ then find the value of $n$.

The correct option is A: $0$
Given expression $\frac{6\times 6^6}{3\times 3^6}÷\frac{4\times 4^6}{2\times 2^6}=2^n$ [$\because a+a+a+a+a=5a$]

$\Rightarrow \frac{6^7}{3^7}÷\frac{4^7}{2^7}=2^n$ [$\because a^m\times a^n=a^{m+n}$, as $6^1\times 6^6=6^{6+1}=6^7$]

$\Rightarrow {\left(\frac{6}{3}\right)}^7÷{\left(\frac{4}{2}\right)}^7=2^n$

$\Rightarrow 2^7÷2^7=2^n$

$\Rightarrow 1=2^n$

$\Rightarrow 2^0=2^n$ [$\because a^0=1$]

$\therefore n=0$ [When bases are same, then power will be equal]