Đáp án:

$\begin{array}{l}
a)A = 0,25.{x^2}{y^3}.\left( { - \dfrac{1}{2}xy} \right)\\
 = \dfrac{1}{4}.\dfrac{{ - 1}}{2}.{x^2}{y^3}.xy\\
 =  - \dfrac{1}{8}{x^3}{y^4}\\
 \Leftrightarrow \left\{ \begin{array}{l}
\text{Bậc}:7\\
\text{Hệ}\,\text{số}:\dfrac{{ - 1}}{8}\\
\text{Biến}:{x^3}{y^4}
\end{array} \right.\\
C = {\left( {\dfrac{{ - 3}}{2}x{y^2}{x^3}} \right)^2}.\left( { - {x^2}y} \right)\\
 = \dfrac{9}{4}{x^8}{y^4}.\left( { - {x^2}y} \right)\\
 = \dfrac{{ - 9}}{4}.{x^{10}}.{y^5}\\
 \Leftrightarrow \left\{ \begin{array}{l}
\text{Bậc}:15\\
\text{Hệ}\,\text{số}: - \dfrac{9}{4}\\
\text{Biến}:{x^{10}}{y^5}
\end{array} \right.\\
E = {\left( { - 0,5{x^7}y} \right)^2}.{\left( { - 2x{y^3}} \right)^5}\\
 = \dfrac{1}{4}{x^{14}}{y^2}.\left( { - 32} \right).{x^5}{y^{15}}\\
 =  - 8{x^{19}}.{y^{17}}\\
 \Leftrightarrow \left\{ \begin{array}{l}
\text{Bậc}:36\\
\text{Hệ}\,\text{số}: - 8\\
\text{Biến}:{x^{18}}{y^{17}}
\end{array} \right.\\
G =  - \dfrac{1}{{25}}x{\left( {\dfrac{1}{3}{x^2}y} \right)^2}.{\left( {\dfrac{5}{2}{y^3}} \right)^2}\\
 = \dfrac{{ - 1}}{{25}}.x.\dfrac{1}{9}{x^4}{y^2}.\dfrac{{25}}{4}.{y^6}\\
 = \dfrac{{ - 1}}{{36}}{x^5}{y^8}\\
\left\{ \begin{array}{l}
\text{Bậc}:13\\
\text{Hệ}\,\text{số}: - \dfrac{1}{{36}}\\
\text{Biến}:{x^5}{y^8}
\end{array} \right.\\
I = a.x.{\left( {x{y^2}} \right)^3}.{\left( { - \dfrac{2}{3}xy} \right)^2}.{\left( { - by} \right)^2}\\
 = a.x.{x^3}{y^6}.\dfrac{4}{9}{x^2}{y^2}.{b^2}{y^2}\\
 = \dfrac{4}{9}a{b^2}.{x^6}{y^{10}}\\
 \Leftrightarrow \left\{ \begin{array}{l}
\text{Bậc}:16\\
\text{Hệ}\,\text{số}:\dfrac{4}{9}a{b^2}\\
\text{Biến}:{x^6}{y^{10}}
\end{array} \right.\\
L = \sqrt {36} {\left( {b{x^2}} \right)^2}.{\left( { - \dfrac{1}{{\sqrt 4 }}b{y^2}} \right)^5}.{\left( { - 3\dfrac{1}{3}xy} \right)^2}\\
 = 6.{b^2}{x^4}.\dfrac{{ - 1}}{{64}}.{b^5}{y^{10}}.{\left( { - \dfrac{{10}}{3}xy} \right)^2}\\
 =  - {b^7}{y^{14}}.\dfrac{{100}}{9}.{x^2}{y^2}\\
 =  - \dfrac{{100}}{9}{b^7}{x^2}{y^{16}}\\
 \Leftrightarrow \left\{ \begin{array}{l}
\text{Bậc}:18\\
\text{Hệ}\,\text{số}:\dfrac{{ - 100}}{9}{b^7}\\
\text{Biến}:{x^2}{y^{16}}
\end{array} \right.\\
b)C > 0\\
 \Leftrightarrow  = \dfrac{{ - 9}}{4}.{x^{10}}.{y^5} > 0\\
 \Leftrightarrow {x^{10}}{y^5} < 0\\
 \Leftrightarrow {y^5} < 0\\
 \Leftrightarrow \left\{ \begin{array}{l}
y < 0\\
x\# 0
\end{array} \right.\\
G < 0\\
 \Leftrightarrow \dfrac{{ - 1}}{{36}}{x^5}{y^8} < 0\\
 \Leftrightarrow {x^5}{y^8} > 0\\
 \Leftrightarrow {x^5} > 0\\
 \Leftrightarrow \left\{ \begin{array}{l}
x > 0\\
y\# 0
\end{array} \right.
\end{array}$