(2x^2y^3)/((-x^2)y^(-2)^-3)

To simplify the given expression, we can follow these steps:<br /><br />$\frac {2x^{2}y^{3}}{(-x^{2}y^{-2})^{-3}}$<br /><br />First, let's simplify the denominator:<br />$(-x^{2}y^{-2})^{-3} = (-1)^{-3} \cdot (x^{2})^{-3} \cdot (y^{-2})^{-3} = -1 \cdot x^{-6} \cdot y^{6} = -x^{-6}y^{6}$<br /><br />Now, we can rewrite the original expression as:<br />$\frac {2x^{2}y^{3}}{-x^{-6}y^{6}}$<br /><br />Next, we can simplify the fraction by multiplying the numerator and denominator by $x^{6}y^{-6}$:<br />$\frac {2x^{2}y^{3} \cdot x^{6}y^{-6}}{-x^{-6}y^{6} \cdot x^{6}y^{-6}} = \frac {2x^{8}y^{-3}}{-1} = -2x^{8}y^{-3}$<br /><br />Therefore, the simplified form of the given expression is $-2x^{8}y^{-3}$.