Solve a^2/a^frac{1{2}a^frac{2{3}}}=

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

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$\frac{a^{2}}{a^{\frac{7}{6}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{7}{6} from 2 to get \frac{5}{6}.

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

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}}{a^{\frac{7}{6}}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{7}{6} from 2 to get \frac{5}{6}.

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

The derivative of ax^{n} is nax^{n-1}.

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

Subtract 1 from \frac{5}{6}.

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