Solve x^3/y^5(x/y^2)^-1

$$\frac { x ^ { 3 } } { y ^ { 5 } } ( \frac { x } { y ^ { 2 } } ) ^ { - 1 }$$

Evaluate

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

Solution Steps

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

$$\frac{x^{3}}{y^{5}}\times \frac{x^{-1}}{\left(y^{2}\right)^{-1}}$$

Multiply \frac{x^{3}}{y^{5}} times \frac{x^{-1}}{\left(y^{2}\right)^{-1}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{3}x^{-1}}{y^{5}\left(y^{2}\right)^{-1}}$$

To multiply powers of the same base, add their exponents. Add 3 and -1 to get 2.

$$\frac{x^{2}}{y^{5}\left(y^{2}\right)^{-1}}$$

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

$$\frac{x^{2}}{y^{5}y^{-2}}$$

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

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

Differentiate w.r.t. x

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