Đáp án:
$\begin{array}{l}
a){27^x}:{3^x} = 9\\
\Rightarrow {\left( {{3^3}} \right)^x}:{3^x} = 9\\
\Rightarrow {3^{3x}}:{3^x} = 9\\
\Rightarrow {3^{3x - x}} = {3^2}\\
\Rightarrow 2x = 2\\
\Rightarrow x = 1\\
b){\left( {x + \dfrac{2}{5}} \right)^3} = \dfrac{1}{{27}} = {\left( {\dfrac{1}{3}} \right)^3}\\
\Rightarrow x + \dfrac{2}{5} = \dfrac{1}{3}\\
\Rightarrow x = \dfrac{1}{3} - \dfrac{2}{5} = - \dfrac{1}{{15}}\\
c){\left( {x + 0,8} \right)^2} = 0,25 = 0,{5^2}\\
\Rightarrow x + 0,8 = 0,5\\
\Rightarrow x = - 0,3\\
a)\dfrac{{{4^{10}}{{.3}^{15}}}}{{{2^{22}}{{.27}^4}}} = \dfrac{{{2^{20}}{{.3}^{15}}}}{{{2^{22}}{{.3}^{12}}}} = \dfrac{{{3^3}}}{{{2^2}}} = \dfrac{{27}}{4}\\
b)\dfrac{{0,{8^5}}}{{0,{4^6}}} = {\left( {\dfrac{{0,8}}{{0,4}}} \right)^5}.\dfrac{1}{{0,4}} = {2^5}.\dfrac{{10}}{4} = {2^3}.10 = 80\\
c)\dfrac{{{{45}^{10}}{{.5}^{20}}}}{{{{75}^{15}}}} = \dfrac{{{{\left( {{3^2}.5} \right)}^{10}}{{.5}^{20}}}}{{{{\left( {{5^2}.3} \right)}^{15}}}}\\
= \dfrac{{{3^{20}}{{.5}^{30}}}}{{{5^{30}}{{.3}^{15}}}} = {3^5}\\
d)\dfrac{{{{20}^5}{{.5}^{10}}}}{{{{100}^5}}} = \dfrac{{{{\left( {{2^2}.5} \right)}^5}{{.5}^{10}}}}{{{{\left( {{2^2}{{.5}^2}} \right)}^5}}}\\
= \dfrac{{{2^{10}}{{.5}^{15}}}}{{{2^{10}}{{.5}^{10}}}} = {5^5}
\end{array}$
