Answer
$\dfrac{x^{16}}{16y^{20}z^{12}}$
Work Step by Step
RECALL:
(i) The products-to-powers rule states that: $(ab)^n=a^nb^n$
(ii) The power rule states that: $(a^m)^n=a^{mn}$
(iii) The negative-exponent rule states that: $a^{-m} = \dfrac{1}{a^m}$ and $\dfrac{1}{a^{-m}} = a^m$
Use the products-to-powers rule to find:
$=(-2)^{-4}(x^{-4})^{-4}(y^{5})^{-4}(z^3)^{-4}$
Use the power rule to find:
$=(-2)^{-4}x^{-4(-4)}y^{5(-4)}z^{3(-4)}
\\=(-2)^{-4}x^{16}y^{-20}z^{-12}$
Use the negative-exponent rule to find:
$=\dfrac{1}{(-2)^4}\cdot x^{16} \dfrac{1}{y^{20}} \cdot \dfrac{1}{z^{12}}
\\=\dfrac{1}{16} \cdot x^{16} \cdot \dfrac{1}{y^{20}} \cdot \dfrac{1}{z^{12}}
\\=\dfrac{x^{16}}{16y^{20}z^{12}}$
