Beginning Algebra With Applications, Chapter 7, 7.2, Section 7.2, Problem 76

Simplify $(a^2 b^2) (-3a b^4)^2$


$
\begin{equation}
\begin{aligned}

\left( a^2 b^2 \right) (-3a b^4)^2 =& \left( a^2 b^2 \right)(-3)^2 \left( a^2 b^8 \right)
&& \text{Multiply each exponent in $-3ab^4$ by the exponent outside the parentheses}
\\
=& \left( a^2 b^2 \right) (9) \left( a^2 b^8 \right)
&& \text{Simplify $(-3)^2$}
\\
=& 9 \left( a^2 \cdot a^2 \right) \left( b^2 \cdot b^8 \right)
&& \text{Use the Properties of Multiplication to rearrange and group factors}
\\
=& 9a^4 b^{10}
&& \text{Multiply variable expressions with the same base by adding the exponents}


\end{aligned}
\end{equation}
$