Solve x^7/2y^1/2/x^3/4y^2

$$\frac { x ^ { 7 / 2 } y ^ { 1 / 2 } } { x ^ { 3 / 4 } y ^ { 2 } }$$

Evaluate

$$\frac{x^{\frac{11}{4}}}{y^{\frac{3}{2}}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{\frac{7}{2}}\sqrt{y}}{x^{\frac{3}{4}}y^{2}}$$

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

$$x^{\frac{7}{2}-\frac{3}{4}}y^{\frac{1}{2}-2}$$

Subtract \frac{3}{4} from \frac{7}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{\frac{11}{4}}y^{\frac{1}{2}-2}$$

Subtract 2 from \frac{1}{2}.

$$x^{\frac{11}{4}}y^{-\frac{3}{2}}$$

Differentiate w.r.t. x

$$\frac{11x^{\frac{7}{4}}}{4y^{\frac{3}{2}}}$$