Solve frac{b^frac{5{4}}}{b^frac{7{6}}}

$$\frac { b ^ { \frac { 5 } { 4 } } } { b ^ { \frac { 7 } { 6 } } }$$

Evaluate

$$\sqrt[12]{b}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{b^{\frac{5}{4}}}{b^{\frac{7}{6}}}$$

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

$$b^{\frac{5}{4}-\frac{7}{6}}$$

Subtract \frac{7}{6} from \frac{5}{4} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\sqrt[12]{b}$$

Differentiate w.r.t. b

$$\frac{1}{12b^{\frac{11}{12}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{\frac{5}{4}-\frac{7}{6}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\sqrt[12]{b})$$

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}.

$$\frac{1}{12}b^{\frac{1}{12}-1}$$

Do the arithmetic.

$$\frac{1}{12}b^{-\frac{11}{12}}$$