Đáp án:
$\begin{array}{l}
a)u{v^2}.\left( { - 5{u^2}v} \right) = - 5{u^3}.{v^3}\\
\Leftrightarrow \left\{ \begin{array}{l}
\text{Hệ số}: - 5\\
\text{Bậc}:6\\
\text{Phần biến}:{u^3}{v^3}
\end{array} \right.\\
b)\left( {\dfrac{{2v}}{{ - 9}}{x^3}{y^8}} \right).{\left( { - 2{x^6}{y^2}} \right)^2}\\
= - \dfrac{2}{9}.v.{x^3}.{y^8}.4{x^{12}}.{y^4}\\
= - \dfrac{2}{9}.4.v.{x^{15}}.{y^{12}}\\
= - \dfrac{8}{9}.v.{x^{15}}.{y^{12}}\\
\Leftrightarrow \left\{ \begin{array}{l}
\text{Hệ số}: - \dfrac{8}{9}\\
\text{Bậc}:1 + 15 + 12 = 28\\
\text{Phần biến}:v.{x^{15}}.{y^{12}}
\end{array} \right.\\
c)\left( {\dfrac{{ - 1}}{7}{x^2}yz} \right).\left( {\dfrac{{ - 2}}{5}x{z^3}} \right).\left( {by} \right)\\
= \dfrac{{ - 1}}{7}.\dfrac{{ - 2}}{5}.b.{x^2}yz.x{z^3}.y\\
= \dfrac{2}{{35}}.b.{x^3}.{y^2}.{z^4}\\
\Leftrightarrow \left\{ \begin{array}{l}
\text{Hệ số}:\dfrac{2}{{35}}.b\\
\text{Bậc}:3 + 2 + 4 = 9\\
\text{Phần biến}:{x^3}{y^2}{z^4}
\end{array} \right.\\
d)5x.\left( { - \dfrac{1}{3}{x^2}{y^5}} \right)\left( {\dfrac{3}{4}xy} \right)\\
= 5.\left( { - \dfrac{1}{3}} \right).\dfrac{3}{4}.x.{x^2}.x.{y^5}.y\\
= - \dfrac{5}{4}.{x^4}{y^6}\\
\Leftrightarrow \left\{ \begin{array}{l}
\text{Hệ số}: - \dfrac{5}{4}\\
\text{Bậc}:10\\
\text{Phần biến}:{x^4}{y^6}
\end{array} \right.\\
e)\left( {x{y^2}} \right)\left( { - \dfrac{3}{4}{x^5}{y^4}} \right).\left( {\dfrac{{ - 8}}{9}.{x^2}{y^2}} \right)\\
= \left( { - \dfrac{3}{4}} \right).\left( { - \dfrac{8}{9}} \right).x{y^2}.{x^5}{y^4}.{x^2}{y^2}\\
= \dfrac{2}{3}.{x^8}.{y^8}\\
\Leftrightarrow \left\{ \begin{array}{l}
\text{Hệ số}:\dfrac{2}{3}\\
\text{Bậc}:16\\
\text{Phần biến}:{x^8}{y^8}
\end{array} \right.\\
f){\left( { - {x^2}} \right)^3}.5.\left( { - xy} \right).{\left( {{\rm{ - ax}}} \right)^3}\\
= - {x^6}.5.\left( { - x} \right).y.\left( { - {a^3}} \right){x^3}\\
= - 5{a^3}.{x^{10}}.y\\
\Leftrightarrow \left\{ \begin{array}{l}
\text{Hệ số}: - 5{a^3}\\
\text{Bậc}:11\\
\text{Phần biến}:{x^{10}}y
\end{array} \right.
\end{array}$
