Solve y^frac{13{9}}divy^frac{5{12}}

$$y ^ { \frac { 13 } { 9 } } \div y ^ { \frac { 5 } { 12 } }$$

Evaluate

$$y^{\frac{37}{36}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{y^{\frac{13}{9}}}{y^{\frac{5}{12}}}$$

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

$$y^{\frac{13}{9}-\frac{5}{12}}$$

Subtract \frac{5}{12} from \frac{13}{9} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$y^{\frac{37}{36}}$$

Differentiate w.r.t. y

$$\frac{37\sqrt[36]{y}}{36}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1}y^{\frac{13}{9}-\frac{5}{12}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{\frac{37}{36}})$$

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}.

$$\frac{37}{36}y^{\frac{37}{36}-1}$$

Do the arithmetic.

$$\frac{37}{36}\sqrt[36]{y}$$