Đáp án:

$\begin{array}{l}
1)a)\dfrac{{{{45}^3}{{.20}^4}{{.18}^2}}}{{{{180}^5}}}\\
 = \dfrac{{{{\left( {{3^2}.5} \right)}^3}.{{\left( {{2^2}.5} \right)}^4}.{{\left( {{{2.3}^2}} \right)}^2}}}{{{{\left( {{2^2}{{.3}^2}.5} \right)}^5}}}\\
 = \dfrac{{{3^6}{{.5}^3}{{.2}^8}{{.5}^4}{{.2}^2}{{.3}^4}}}{{{2^{10}}{{.3}^{10}}{{.5}^5}}}\\
 = {5^2} = 25\\
b)\dfrac{{{2^{13}} + {2^5}}}{{{2^{10}} + {2^2}}} = \dfrac{{{2^5}\left( {{2^8} + 1} \right)}}{{{2^2}\left( {{2^8} + 1} \right)}} = {2^3} = 8\\
B2)a)50 - 5\left( {x - 3} \right) = 30\\
 \Rightarrow 5\left( {x - 3} \right) = 50 - 30\\
 \Rightarrow 5\left( {x - 3} \right) = 20\\
 \Rightarrow x - 3 = 4\\
 \Rightarrow x = 7\\
Vậy\,x = 7\\
b)14 + {5^2}.x = {4^6}:{4^3}\\
 \Rightarrow 14 + 25.x = {4^3}\\
 \Rightarrow 14 + 25.x = 64\\
 \Rightarrow 25.x = 50\\
 \Rightarrow x = 2\\
Vậy\,x = 2\\
c)x \vdots 12;x \vdots 25;x \vdots 30\left( {500 < x < 700} \right)\\
 \Rightarrow x = BC\left( {12;25;30} \right)\\
Do:12 = {2^2}.3;25 = {5^2};30 = 2.3.5\\
 \Rightarrow BCNN\left( {12;25;30} \right) = {2^2}{.3.5^2} = 300\\
 \Rightarrow x \in \left\{ {300;600;900;...} \right\}\\
 \Rightarrow x = 600\left( {do:500 < x < 700} \right)\\
Vậy\,x = 600\\
d)\left( {x + 4} \right) \vdots \left( {x + 1} \right)\\
 \Rightarrow \left( {x + 1 + 3} \right) \vdots \left( {x + 1} \right)\\
 \Rightarrow 3 \vdots \left( {x + 1} \right)\\
 \Rightarrow \left( {x + 1} \right) \in \left\{ { - 3; - 1;1;3} \right\}\\
 \Rightarrow x \in \left\{ { - 4; - 2;0;2} \right\}
\end{array}$