Solve x^10/x^4y^4/y^10

$$\frac { x ^ { 10 } } { x ^ { 4 } } \frac { y ^ { 4 } } { y ^ { 10 } }$$

Evaluate

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

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 10 to get 6.

$$x^{6}\times \frac{y^{4}}{y^{10}}$$

Rewrite y^{10} as y^{4}y^{6}. Cancel out y^{4} in both numerator and denominator.

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

Express x^{6}\times \frac{1}{y^{6}} as a single fraction.

$$\frac{x^{6}}{y^{6}}$$

Differentiate w.r.t. x

$$\frac{6x^{5}}{y^{6}}$$