Answer
$$-\frac{x^{13}}{8y^{16}}$$
Work Step by Step
$$(-4x^{-4}y^{5})^{-2}(-2x^{5}y^{-6})$$
Simplify the first term $(-4x^{-4}y^{5})^{-2}$
Recall the power rule: $(a^{m})^{n}=a^{mn}$
Thus,
$$(-4x^{-4}y^{5})^{-2} = -4^{-2}x^{(-4)(-2)}y^{5(-2)}=-4^{-2}x^{8}y^{-10}$$
Rewrite the equation:
$$(-4^{-2}x^{8}y^{-10})(-2x^{5}y^{-6})$$
Recall the product rule: $a^{m}⋅a^{n}=a^{m+n}$
Thus,
$$(-4^{-2}x^{8}y^{-10})(-2x^{5}y^{-6}) = (-4^{-2})(-2)(x^{8+5}y^{-10-6}) = (-4^{-2})(-2)(x^{13}y^{-16})$$
Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$
Thus,
$$(-4^{-2})(-2)(x^{13}y^{-16}) = \frac{(-2)(x^{13})}{-4^{2}y^{16}}$$
$$= \frac{-2x^{13}}{16y^{16}}$$
$$= \frac{-x^{13}}{8y^{16}}$$
Using the fraction rule: $\frac{-a}{b} = -\frac{a}{b}$
$$\frac{-x^{13}}{8y^{16}} = -\frac{x^{13}}{8y^{16}}$$
