Solve frac{y^frac{16{9}}}{y^frac{1{12}}}

$$\frac { y ^ { \frac { 16 } { 9 } } } { y ^ { \frac { 1 } { 12 } } }$$

Evaluate

$$y^{\frac{61}{36}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{\frac{16}{9}}}{\sqrt[12]{y}}$$

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

$$y^{\frac{16}{9}-\frac{1}{12}}$$

Subtract \frac{1}{12} from \frac{16}{9} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$y^{\frac{61}{36}}$$

Differentiate w.r.t. y

$$\frac{61y^{\frac{25}{36}}}{36}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{\frac{16}{9}-\frac{1}{12}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{\frac{61}{36}})$$

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}.

$$\frac{61}{36}y^{\frac{61}{36}-1}$$

Do the arithmetic.

$$\frac{61}{36}y^{\frac{25}{36}}$$