Solve frac{y^frac{5{4}}}{y^frac{1{4}}}

$$\frac { y ^ { \frac { 5 } { 4 } } } { y ^ { \frac { 1 } { 4 } } }$$

Evaluate

$$y$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{\frac{5}{4}}}{\sqrt[4]{y}}$$

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

$$y^{\frac{5}{4}-\frac{1}{4}}$$

Subtract \frac{1}{4} from \frac{5}{4} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$y^{1}$$

For any term t, t^{1}=t.

$$y$$

Differentiate w.r.t. y

$$1$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{\frac{5}{4}-\frac{1}{4}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$y^{1-1}$$

Do the arithmetic.

$$y^{0}$$

For any term t except 0, t^{0}=1.

$$1$$