Solve frac{x^{2}}{y^2}div(xy)^0/(xy^3)^2

$$\frac { x ^ { 2 } } { y ^ { 2 } } \div \frac { ( x y ) ^ { 0 } } { ( x y ^ { 3 } ) ^ { 2 } }$$

Evaluate

$$\left(xy\right)^{4}$$

Solution Steps

Divide \frac{x^{2}}{y^{2}} by \frac{\left(xy\right)^{0}}{\left(xy^{3}\right)^{2}} by multiplying \frac{x^{2}}{y^{2}} by the reciprocal of \frac{\left(xy\right)^{0}}{\left(xy^{3}\right)^{2}}.

$$\frac{x^{2}\left(xy^{3}\right)^{2}}{y^{2}\left(xy\right)^{0}}$$

Expand \left(xy^{3}\right)^{2}.

$$\frac{x^{2}x^{2}\left(y^{3}\right)^{2}}{y^{2}\left(xy\right)^{0}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{x^{2}x^{2}y^{6}}{y^{2}\left(xy\right)^{0}}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{x^{4}y^{6}}{y^{2}\left(xy\right)^{0}}$$

Calculate xy to the power of 0 and get 1.

$$\frac{x^{4}y^{6}}{y^{2}\times 1}$$

Cancel out y^{2} in both numerator and denominator.

$$x^{4}y^{4}$$

Differentiate w.r.t. x

$$4x^{3}y^{4}$$