Đáp án:
$\begin{array}{l}
d)\dfrac{{{5^{102}} + {5^{109}}}}{{{5^{104}} + {5^{111}}}} = \dfrac{{{5^{102}}\left( {1 + {5^7}} \right)}}{{{5^{104}}.\left( {1 + {5^7}} \right)}} = \dfrac{1}{{{5^2}}} = \dfrac{1}{{25}}\\
e)\dfrac{1}{7} + \dfrac{6}{7}.\left( {\dfrac{1}{2} - \dfrac{1}{3}} \right)\\
= \dfrac{1}{7} + \dfrac{6}{7}.\dfrac{1}{6}\\
= \dfrac{1}{7} + \dfrac{1}{7}\\
= \dfrac{2}{7}\\
f)\sqrt 9 .\left( {\dfrac{3}{{\sqrt {81} }} + \dfrac{2}{3} - 2} \right) + {\left( {\dfrac{5}{2}} \right)^5}.{\left( {\dfrac{4}{5}} \right)^5}\\
= 3.\left( {\dfrac{3}{9} + \dfrac{2}{3} - 2} \right) + \dfrac{{{5^5}}}{{{2^5}}}.\dfrac{{{4^5}}}{{{5^5}}}\\
= 3.\left( {\dfrac{1}{3} + \dfrac{2}{3} - 2} \right) + {\left( {\dfrac{4}{2}} \right)^5}\\
= 3.\left( {1 - 2} \right) + {2^5}\\
= 3.\left( { - 1} \right) + 32\\
= 29
\end{array}$
