Answer
$4^{24}y^{24}$
Work Step by Step
We are given the expression $(-4^{-6}y^{-6})^{-4}$.
To simplify, we can use the power of a product rule, which holds that $(ab)^{m}=a^{m}b^{m}$ (where a and b are real numbers, and m is an integer).
Recall that the negative sign should be treated as a separate term.
$(-4^{-6}y^{-6})^{-4}=(-1)^{-4}\times(4^{-6})^{-4}\times(y^{-6})^{-4}$
Next, we can use the power rule, which holds that $(a^{m})^{n}=a^{m\times n}$ (where a is a real number, and m and n are integers).
$((-1)^{-4})\times(4^{-6\times-4})\times(y^{-6\times-4})=((-1)^{-4})\times(4^{24})\times(y^{24})=1\times4^{24}\times y^{24}=4^{24}y^{24}$
