Answer
$\dfrac{(-3x^{2}y^{2})^{-2}}{(xyz)^{-2}}=\dfrac{z^{2}}{9x^{2}y^{2}}$
Work Step by Step
$\dfrac{(-3x^{2}y^{2})^{-2}}{(xyz)^{-2}}$
Evaluate the exponential expressions in the numerator and the denominator:
$\dfrac{(-3x^{2}y^{2})^{-2}}{(xyz)^{-2}}=\dfrac{(-3)^{-2}x^{-4}y^{-4}}{x^{-2}y^{-2}z^{-2}}=...$
Evaluate the division and simplify:
$...=\dfrac{1}{(-3)^{2}}\cdot\dfrac{x^{-4-(-2)}y^{-4-(-2)}}{z^{-2}}=\dfrac{1}{9}\cdot\dfrac{x^{-2}y^{-2}}{z^{-2}}=\dfrac{z^{2}}{9x^{2}y^{2}}$
