Given the expression;
[tex](n^{-7}p^7)^{-8}[/tex]First, we expand the expression using the indices rule that;
[tex](ab)^c=a^cb^c[/tex]So, the expression is;
[tex](n^{-7}p^7)^{-8}=(n^{-7})^{-8}\times(p^7)^{-8}[/tex]So, we apply another rule;
[tex](a^b)=a^{b\times c}=a^{bc}[/tex]Thus, we have;
[tex]\begin{gathered} (n^{-7})^{-8}\times(p^7)^{-8}=n^{56}\times p^{-56} \\ (n^{-7}p^7)^{-8}=n^{56}p^{-56} \end{gathered}[/tex]Then, we have;
[tex]\begin{gathered} n^{56}p^{-56}=\frac{n^{56}}{p^{56}} \\ n^{56}p^{-56}=(\frac{n}{p})^{56} \end{gathered}[/tex]