Answer
$-64y^{3}$
Work Step by Step
We are given the expression $(-2^{-2}y^{-1})^{-3}$.
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.
$(-2^{-2}y^{-1})^{-3}=(-1)^{-3}\times(2^{-2})^{-3}\times(y^{-1})^{-3}$
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).
$((-1)^{-3})\times(2^{-2\times-3})\times(y^{-1\times-3})=((-1)^{-3})\times(2^{6})\times(y^{3})=-64y^{3}$
