Solve frac{{y}^frac{7{10}}}{{y}^frac{1{5}}}

$$\frac{ { y }^{ \frac{ 7 }{ 10 } } }{ { y }^{ \frac{ 1 }{ 5 } } }$$

Evaluate

$$\sqrt{y}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{\frac{7}{10}}}{\sqrt[5]{y}}$$

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

$$y^{\frac{7}{10}-\frac{1}{5}}$$

Subtract \frac{1}{5} from \frac{7}{10} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\sqrt{y}$$

Differentiate w.r.t. y

$$\frac{1}{2\sqrt{y}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{\frac{7}{10}-\frac{1}{5}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\sqrt{y})$$

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}.

$$\frac{1}{2}y^{\frac{1}{2}-1}$$

Do the arithmetic.

$$\frac{1}{2}y^{-\frac{1}{2}}$$