[tex] \bf \boxed{-\sqrt{16a^4b^6}}\implies -\sqrt{4^2(a^2)^2(b^3)^2}\implies -4a^2b^3\implies \boxed{-4a^2|b^3|}
\\\\\\
\boxed{\sqrt[3]{-16a^4b^7}}~~
\begin{cases}
16=2\cdot 2\cdot 2\cdot 2\\
\qquad 2^3\cdot 2\\
a^4=a^{3+1}\\
\qquad a^3a^1\\
b^7=b^{2\cdot 3+1}\\
\qquad (b^2)^3b^1
\end{cases}\implies \sqrt[3]{-2^3\cdot 2a^3a^1(b^2)^3b^1}
\\\\\\
-2a(b^2)\sqrt[3]{2a^1b^1}\implies \boxed{-2ab^2\sqrt[3]{2ab}} [/tex]
[tex] \bf \boxed{\sqrt[3]{16a^4b^6}}~~
\begin{cases}
16=2\cdot 2\cdot 2\cdot 2\\
\qquad 2^3\cdot 2\\
a^4=a^{3+1}\\
\qquad a^3a^1\\
b^6=b^{2\cdot 3}\\
\qquad (b^2)^3
\end{cases}\implies \sqrt[3]{2^3\cdot 2a^3a(b^2)^3}
\\\\\\
\boxed{2ab^2\sqrt[3]{2a}} [/tex]
