Question

I need help with this problem

Answer 1

$\bf \begin{cases} (n^4)^p=n^{12}\to &n^{4\cdot p}=n^{12}\to 4p=12 \\ &\qquad \uparrow \\ &\textit{same bases, thus}\\ &\qquad \downarrow \\ n^3\cdot n^q=n^6\to &n^{3+q}=n^6\to 3+q=6 \end{cases} \\\\\\ thus\implies \begin{cases} 4p=12\implies p=\frac{12}{4} \\\\ 3+q=6\implies q=6-3 \end{cases} \\\\ \\\\ then\implies p\cdot q=\boxed{?}$