Answer
$$(3x^{4}y^{-2})(-2x^{5}y^{-3})=-\frac{6x^{9}}{y^{5}}$$
Work Step by Step
$$(3x^{4}y^{-2})(-2x^{5}y^{-3})$$
Recall the product rule: $a^{m}⋅a^{n}=a^{m+n}$
Thus,
$$(3x^{4}y^{-2})(-2x^{5}y^{-3})$$ $$(3(-2)x^{4+5}y^{-2+(-3)})$$ $$(-6x^{9}y^{-5})$$
Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}} = a^{n}$ and the zero exponent rule: $b^{0}=1$
Thus,
$$(-6x^{9}y^{-5}) = \frac{-6x^{9}}{y^{5}} = -\frac{6x^{9}}{y^{5}}$$
