[tex]\displaystyle \bf \\
\frac{8^{37}\times 81^{25}}{16^{27}\times 27^{33}}=\frac{\Big(2^3\Big)^{37}\times \Big(3^4\Big)^{25}}{\Big(2^4\Big)^{27}\times \Big(3^3\Big)^{33}}=\\\\\\
=\frac{2^{3\times37}\times 3^{4\times 25}}{2^{4\times 27}\times 3^{3\times 33}}=\frac{2^{111}\times 3^{100}}{2^{108}\times 3^{99}}=\\\\
=2^{111-108}\times 3^{100-99} = 2^3 \times 3^1 = 8\times 3 = \boxed{\bf24}[/tex]
