Đáp án:

$\begin{array}{l}
a)\dfrac{{32}}{{{2^n}}} = 2\\
 \Leftrightarrow {2^{5 - n}} = 2\\
 \Leftrightarrow 5 - n = 1\\
 \Leftrightarrow n = 4\\
Vậy\,n = 4\\
b)\dfrac{{{8^n}}}{{{2^n}}} = 16\\
 \Leftrightarrow \dfrac{{{2^{3n}}}}{{{2^n}}} = {2^4}\\
 \Leftrightarrow {2^{3n - n}} = {2^4}\\
 \Leftrightarrow 2n = 4\\
 \Leftrightarrow n = 2\\
Vậy\,n = 2\\
c)\dfrac{{{{33}^{2n}}}}{{{{11}^{2n}}}} = 81\\
 \Leftrightarrow {\left( {\dfrac{{33}}{{11}}} \right)^{2n}} = {3^4}\\
 \Leftrightarrow {3^{2n}} = {3^4}\\
 \Leftrightarrow 2n = 4\\
 \Leftrightarrow n = 2\\
Vậy\,n = 2\\
d)\dfrac{{54}}{{{3^{n - 2}}}} = 2\\
 \Leftrightarrow {3^{n - 2}} = 54:2 = 27\\
 \Leftrightarrow {3^{n - 2}} = {3^3}\\
 \Leftrightarrow n - 2 = 3\\
 \Leftrightarrow n = 5\\
Vậy\,n = 5\\
e)\dfrac{{175}}{{{5^{n + 1}}}} = 7\\
 \Leftrightarrow {5^{n + 1}} = 175:7 = 25\\
 \Leftrightarrow {5^{n + 1}} = {5^2}\\
 \Leftrightarrow n + 1 = 2\\
 \Leftrightarrow n = 1\\
Vậy\,n = 1\\
f)\dfrac{{135}}{{{3^{n - 2}}}} = 5\\
 \Leftrightarrow {3^{n - 2}} = 135:5 = 27\\
 \Leftrightarrow {3^{n - 2}} = {3^3}\\
 \Leftrightarrow n - 2 = 3\\
 \Leftrightarrow n = 5\\
Vậy\,n = 5\\
g)\dfrac{{64}}{{{2^{n + 1}}}} = 8\\
 \Leftrightarrow {2^{n + 1}} = 8\\
 \Leftrightarrow {2^{n + 1}} = {2^3}\\
 \Leftrightarrow n + 1 = 3\\
 \Leftrightarrow n = 2\\
Vậy\,n = 2\\
h)\dfrac{{{3^8}}}{{{3^n}}} = {3^{20}}\\
 \Leftrightarrow {3^{8 - n}} = {3^{20}}\\
 \Leftrightarrow 8 - n = 20\\
 \Leftrightarrow n =  - 12\\
Vậy\,n =  - 12\\
i)\dfrac{{{3^5}}}{{{3^n}}} = {3^{10}}\\
 \Leftrightarrow {3^{5 - n}} = {3^{10}}\\
 \Leftrightarrow 5 - n = 10\\
 \Leftrightarrow n =  - 5\\
Vậy\,n =  - 5\\
j)\dfrac{{{5^5}}}{{{5^n}}} = {5^{18}}\\
 \Leftrightarrow {5^{5 - n}} = {5^{18}}\\
 \Leftrightarrow 5 - n = 18\\
 \Leftrightarrow n =  - 13\\
Vậy\,n =  - 13\\
k)\dfrac{{{2^3}}}{{{2^n}}} = {4^5}\\
 \Leftrightarrow {2^{3 - n}} = {2^{2.5}}\\
 \Leftrightarrow 3 - n = 10\\
 \Leftrightarrow n =  - 7\\
Vậy\,n =  - 7\\
i){3^x} = \dfrac{{{9^8}}}{{{{27}^3}{{.81}^2}}}\\
 \Leftrightarrow {3^x} = \dfrac{{{3^{2.8}}}}{{{3^{3.3}}{{.3}^{4.2}}}}\\
 \Leftrightarrow {3^x} = {3^{16 - 9 - 8}}\\
 \Leftrightarrow {3^x} = {3^{ - 1}}\\
 \Leftrightarrow x =  - 1\\
Vậy\,x =  - 1
\end{array}$