Đáp án:
$\begin{array}{l}
M = \frac{{{8^{20}} + {4^{20}}}}{{{4^{25}} + {{64}^5}}} = \frac{{{{\left( {{2^3}} \right)}^{20}} + {{\left( {{2^2}} \right)}^{20}}}}{{{{\left( {{2^2}} \right)}^{25}} + {{\left( {{2^6}} \right)}^5}}}\\
= \frac{{{2^{60}} + {2^{40}}}}{{{2^{50}} + {2^{30}}}} = \frac{{{2^{40}}\left( {{2^{20}} + 1} \right)}}{{{2^{20}}\left( {{2^{20}} + 1} \right)}}\\
= \frac{{{2^{40}}}}{{{2^{20}}}} = {2^{40 - 20}}\\
= {2^{20}}\\
T = \frac{{{{45}^{10}}{{.5}^{20}}}}{{{{75}^{15}}}}\\
= \frac{{{{\left( {{3^2}.5} \right)}^{10}}{{.5}^{20}}}}{{{{\left( {{{3.5}^2}} \right)}^{15}}}}\\
= \frac{{{3^{20}}{{.5}^{10}}{{.5}^{20}}}}{{{3^{15}}{{.5}^{30}}}}\\
= {3^{20 - 15}}{.5^{10 + 20 - 30}}\\
= {3^5}{.5^0}\\
= {3^5}
\end{array}$
