Solve (x^-2*y^-1/y^-3*x)^-1

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

Evaluate

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

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

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

Differentiate w.r.t. x

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