Solve frac{a^frac{2{3}}}{a^-frac{1{6}}}=

$$\frac { a ^ { \frac { 2 } { 3 } } } { a ^ { - \frac { 1 } { 6 } } } =$$

Differentiate w.r.t. a

$$\frac{5}{6\sqrt[6]{a}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{\frac{2}{3}-\left(-\frac{1}{6}\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{5}{6}})$$

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}.

$$\frac{5}{6}a^{\frac{5}{6}-1}$$

Do the arithmetic.

$$\frac{5}{6}a^{-\frac{1}{6}}$$

Evaluate

$$a^{\frac{5}{6}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -\frac{1}{6} from \frac{2}{3} to get \frac{5}{6}.

$$a^{\frac{5}{6}}$$