Which expression is equivalent to (2x^-3y²)^-2 for x, y ≠ 0?

Apply the outer exponent $-2$ to each factor: $2^{-2}=\frac{1}{4}$, $(x^{-3})^{-2}=x^{6}$, and $(y^2)^{-2}=y^{-4}=\frac{1}{y^4}$. Combined, the expression is $\frac{x^6}{4y^4}$, choice F. Choice G has the $x$ term in the denominator and puts $4$ in the numerator, so it mishandles every sign. Choice H keeps $x^{-6}$, so the exponent of $x$ was multiplied incorrectly ($-3\cdot-2=+6$, not $-6$). Choice J drops the negative outer exponent, which squares the coefficient and flips nothing. Multiply exponents carefully, with signs.