Bài giải :

$\frac{{{4}^{5}}+{{4}^{5}}+{{4}^{5}}+{{4}^{5}}}{{{3}^{5}}+{{3}^{5}}+{{3}^{5}}}.\frac{{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}}{{{2}^{5}}+{{2}^{5}}}={{2}^{n}}$

$\frac{{{4.4}^{5}}}{{{3.3}^{5}}}.\frac{{{6.6}^{5}}}{{{2.2}^{5}}}={{2}^{n}}$

$\frac{{{4}^{6}}}{{{3}^{6}}}.\frac{{{6}^{6}}}{{{2}^{6}}}={{2}^{n}}$

${{\left( \frac{4.6}{3.2} \right)}^{6}}={{2}^{n}}$

${{4}^{6}}={{2}^{n}}$

${{2}^{12}}={{2}^{n}}$

n = 12.