Solve frac{x^frac{2{5}}y^frac{4{5}}}{x^frac{5{6}}y^frac{2{5}}}=

$$\frac { x ^ { \frac { 2 } { 5 } } y ^ { \frac { 4 } { 5 } } } { x ^ { \frac { 5 } { 6 } } y ^ { \frac { 2 } { 5 } } } =$$

Evaluate

$$\frac{y^{\frac{2}{5}}}{x^{\frac{13}{30}}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{\frac{2}{5}}y^{\frac{4}{5}}}{x^{\frac{5}{6}}y^{\frac{2}{5}}}$$

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

$$x^{\frac{2}{5}-\frac{5}{6}}y^{\frac{4}{5}-\frac{2}{5}}$$

Subtract \frac{5}{6} from \frac{2}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{-\frac{13}{30}}y^{\frac{4}{5}-\frac{2}{5}}$$

Subtract \frac{2}{5} from \frac{4}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{-\frac{13}{30}}y^{\frac{2}{5}}$$

Differentiate w.r.t. x

$$-\frac{13y^{\frac{2}{5}}}{30x^{\frac{43}{30}}}$$