-2a^4b(-3ab^5(5a^-3b^-7) simplify

-2a^4b(-3ab^5(5a^-3b^-7) ) simplify

$$\small$\text{$
\begin{array}{rcl}
-2a^4\cdot b \left [-3\cdot ab^5 ( 5a^{-3}\cdot b^{-7} ) \right] \\\\
&=& -2a^4\cdot b \left (-3\cdot 5 \cdot a\cdot a^{-3}\cdot b^5 \cdot b^{-7} \right) \\\\
&=& -2a^4\cdot b \left (-15\cdot a^{1-3}\cdot b^{5-7} \right) \\\\
&=& -2a^4\cdot b \left (-15\cdot a^{-2}\cdot b^{-2} \right) \\\\
&=& (-2)\cdot(-15)\cdot a^4\cdot b \cdot a^{-2}\cdot b^{-2} \right) \\\\
&=& 30\cdot a^4\cdot b \cdot a^{-2}\cdot b^{-2} \\\\
&=& 30\cdot a^4\cdot a^{-2} \cdot b \cdot b^{-2} \\\\
&=& 30\cdot a^{4-2} \cdot b^{1-2} \\\\
&=& 30\cdot a^{2} \cdot b^{-1}
\end{array}
$}}$$