Answer
$\Big(\dfrac{x^{-2}y^{4}z^{0}}{x^{3}y^{7}}\Big)^{2}=\dfrac{1}{x^{10}y^{6}}$
Work Step by Step
$\Big(\dfrac{x^{-2}y^{4}z^{0}}{x^{3}y^{7}}\Big)^{2}$
First, note that $z^{0}=1$, so this expression can be rewritten as:
$\Big(\dfrac{x^{-2}y^{4}z^{0}}{x^{3}y^{7}}\Big)^{2}=\Big(\dfrac{x^{-2}y^{4}}{x^{3}y^{7}}\Big)^{2}=...$
Evaluate the exponential expression:
$...=\dfrac{x^{-4}y^{8}}{x^{6}y^{14}}=...$
Evaluate the division:
$...=x^{-4-6}y^{8-14}=x^{-10}y^{-6}=\dfrac{1}{x^{10}y^{6}}$
