Đáp án:
$\begin{array}{l}
a)A = \dfrac{{{2^{12}}{{.3}^5} - {4^6}{{.9}^2}}}{{{{\left( {{2^2}.3} \right)}^6} + {8^4}{{.3}^5}}} - \dfrac{{{5^{10}}{{.7}^3} - {{25}^5}{{.49}^2}}}{{{{\left( {125.7} \right)}^3} + {5^9}{{.14}^3}}}\\
= \dfrac{{{2^{12}}{{.3}^5} - {2^{12}}{{.3}^4}}}{{{2^{12}}{{.3}^6} + {2^{12}}{{.3}^5}}} - \dfrac{{{5^{10}}{{.7}^3} - {5^{10}}{{.7}^4}}}{{{5^9}{{.7}^3} + {5^9}{{.2}^3}{{.7}^3}}}\\
= \dfrac{{{2^{12}}{{.3}^4}\left( {3 - 1} \right)}}{{{2^{12}}{{.3}^5}.\left( {3 + 1} \right)}} - \dfrac{{{5^{10}}{{.7}^3}\left( {1 - 7} \right)}}{{{5^9}{{.7}^3}\left( {1 + {2^3}} \right)}}\\
= \dfrac{2}{{3.4}} - \dfrac{{5.\left( { - 6} \right)}}{9}\\
= \dfrac{1}{6} + \dfrac{{10}}{3}\\
= \dfrac{{21}}{6} = \dfrac{7}{2}\\
b){3^{n + 2}} - {2^{n + 2}} + {3^n} - {2^n}\\
= {9.3^n} - {4.2^n} + {3^n} - {2^n}\\
= {10.3^n} - {5.2^n}\\
= {10.3^n} - {5.2^{n - 1}}.2\\
= 10.\left( {{3^n} - {2^{n - 1}}} \right) \vdots 10
\end{array}$
