Answer:
Simplifying the given expression we have;
[tex]-(m^4n^{-8})=-\frac{m^4}{n^8}[/tex]Explanation:
Given the expression;
[tex]-(mn^{-2})^4[/tex]Recall that form the laws of exponents;
[tex](x^a)^b=x^{a\times b}[/tex]So, for the given expression;
[tex]\begin{gathered} -(mn^{-2})^4=-(m)^4(n^{-2})^4 \\ =-(m^4\cdot n^{-2\times4}) \\ =-(m^4n^{-8}) \end{gathered}[/tex]Therefore, simplifying the expression we have;
[tex]-(m^4n^{-8})=-\frac{m^4}{n^8}[/tex]