Beginning Algebra With Applications, Chapter 7, 7.2, Section 7.2, Problem 80

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


$
\begin{equation}
\begin{aligned}

(-3a^2b)^3 (-3ab)^3 =& (-3)^3 \left( a^6 b^3 \right) (-3)^3 \left( a^3 b^3 \right)
&& \text{Multiply each exponent in $-3a^2b$ and $-3ab$ by the exponent outside the parentheses}
\\
=& (-27) \left( a^6 b^3 \right) (-27) \left( a^3 b^3 \right)
&& \text{Simplify $(-3)^3$}
\\
=& [-27 \cdot (-27)] \left( a^6 \cdot a^3 \right) \left( b^3 \cdot b^3 \right)
&& \text{Use the Properties of Multiplication to rearrange and group factors}
\\
=& 729 a^9 b^6
&& \text{Multiply variable expressions with the same base by adding the exponents}


\end{aligned}
\end{equation}
$

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