Answer
$$(x^{-4n} \cdot x^{n})^{-3}= x^{9n}$$
Work Step by Step
$$(x^{-4n} \cdot x^{n})^{-3}$$
Recall the Products to Powers rule: $(ab)^{n} = a^{n}\cdot b^{n}$
Thus,
$$(x^{-4n} \cdot x^{n})^{-3}$$ $$=x^{(-4n)(-3)} \cdot x^{(n)(-3)}$$ $$=x^{12n} \cdot x^{-3n}$$
Recall the product rule: $a^{m}⋅a^{n}=a^{m+n}$
Thus,
$$x^{12n} \cdot x^{-3n} = x^{9n}$$
