How do you simplify (t^-2)^-4?

Use the rule for exponents: $\textcolor{red}{{\left({x}^{a}\right)}^{b} = {x}^{a \times b}}$
${\left({t}^{-} 2\right)}^{-} 4 = {t}^{- 2 \times - 4} = {t}^{8}$