Apply the property of the product of two powers of the same base in reverse: $a^{m+n}=a^m\cdot a^n$

Rewrite $\frac{2^{2n}4^{2n}}{8^{-1}8^{2n}}$ using the property of the power of a quotient: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

Divide $2$ by $8$

Divide fractions $\frac{\left(\frac{1}{4}\right)^{2n}4^{2n}}{\frac{1}{8}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$