Solve frac{b^frac{5{12}}}{b^frac{13{15}}}

$$\frac { b ^ { \frac { 5 } { 12 } } } { b ^ { \frac { 13 } { 15 } } }$$

Evaluate

$$\frac{1}{b^{\frac{9}{20}}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{b^{\frac{5}{12}}}{b^{\frac{13}{15}}}$$

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

$$b^{\frac{5}{12}-\frac{13}{15}}$$

Subtract \frac{13}{15} from \frac{5}{12} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$b^{-\frac{9}{20}}$$

Differentiate w.r.t. b

$$-\frac{9}{20b^{\frac{29}{20}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{\frac{5}{12}-\frac{13}{15}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{-\frac{9}{20}})$$

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}.

$$-\frac{9}{20}b^{-\frac{9}{20}-1}$$

Do the arithmetic.

$$-\frac{9}{20}b^{-\frac{29}{20}}$$