Solve frac{a^frac{6{7}}}{a^frac{1{4}}}

$$\frac { a ^ { \frac { 6 } { 7 } } } { a ^ { \frac { 1 } { 4 } } }$$

Evaluate

$$a^{\frac{17}{28}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{\frac{6}{7}}}{\sqrt[4]{a}}$$

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

$$a^{\frac{6}{7}-\frac{1}{4}}$$

Subtract \frac{1}{4} from \frac{6}{7} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$a^{\frac{17}{28}}$$

Differentiate w.r.t. a

$$\frac{17}{28a^{\frac{11}{28}}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{17}{28}})$$

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}.

$$\frac{17}{28}a^{\frac{17}{28}-1}$$

Do the arithmetic.

$$\frac{17}{28}a^{-\frac{11}{28}}$$