Solve frac{y^frac{12{10}}}{y^frac{9{10}}}=

$$\frac { y ^ { \frac { 12 } { 10 } } } { y ^ { \frac { 9 } { 10 } } } =$$

Evaluate

$$y^{\frac{3}{10}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{\frac{6}{5}}}{y^{\frac{9}{10}}}$$

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

$$y^{\frac{6}{5}-\frac{9}{10}}$$

Subtract \frac{9}{10} from \frac{6}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$y^{\frac{3}{10}}$$

Differentiate w.r.t. y

$$\frac{3}{10y^{\frac{7}{10}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{\frac{6}{5}-\frac{9}{10}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{\frac{3}{10}})$$

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}.

$$\frac{3}{10}y^{\frac{3}{10}-1}$$

Do the arithmetic.

$$\frac{3}{10}y^{-\frac{7}{10}}$$