Solve y:x^{2}yx^-5y^-4x^5x^0

$$y : x ^ { 2 } y x ^ { - 5 } y ^ { - 4 } x ^ { 5 } x ^ { 0 }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$\frac{y}{x^{2}}y^{-3}x^{-5}x^{5}x^{0}$$

Multiply x^{-5} and x^{5} to get 1.

$$\frac{y}{x^{2}}y^{-3}x^{0}$$

Calculate x to the power of 0 and get 1.

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

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

$$\frac{yy^{-3}}{x^{2}}\times 1$$

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

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

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

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

Differentiate w.r.t. x

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