Solve (-3/xy^2)^-1

$$( \frac { - 3 } { x y ^ { 2 } } ) ^ { - 1 }$$

Evaluate

$$-\frac{xy^{2}}{3}$$

Solution Steps

To raise \frac{-3}{xy^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-3\right)^{-1}}{\left(xy^{2}\right)^{-1}}$$

Calculate -3 to the power of -1 and get -\frac{1}{3}.

$$\frac{-\frac{1}{3}}{\left(xy^{2}\right)^{-1}}$$

Expand \left(xy^{2}\right)^{-1}.

$$\frac{-\frac{1}{3}}{x^{-1}\left(y^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{-\frac{1}{3}}{x^{-1}y^{-2}}$$

Express \frac{-\frac{1}{3}}{x^{-1}y^{-2}} as a single fraction.

$$\frac{-1}{3x^{-1}y^{-2}}$$

Differentiate w.r.t. x

$$-\frac{y^{2}}{3}$$