Solve (19a^frac{2{3}})a^frac{3{3}}=

$$( 19 a ^ { \frac { 2 } { 3 } } ) a ^ { \frac { 3 } { 3 } } =$$

Evaluate

$$19a^{\frac{5}{3}}$$

Solution Steps

Divide 3 by 3 to get 1.

$$19a^{\frac{2}{3}}a^{1}$$

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and 1 to get \frac{5}{3}.

$$19a^{\frac{5}{3}}$$

Differentiate w.r.t. a

$$\frac{95a^{\frac{2}{3}}}{3}$$

Steps Using Definition of a Derivative

Divide 3 by 3 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(19a^{\frac{2}{3}}a^{1})$$

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and 1 to get \frac{5}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(19a^{\frac{5}{3}})$$

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

$$\frac{5}{3}\times 19a^{\frac{5}{3}-1}$$

Multiply \frac{5}{3} times 19.

$$\frac{95}{3}a^{\frac{5}{3}-1}$$

Subtract 1 from \frac{5}{3}.

$$\frac{95}{3}a^{\frac{2}{3}}$$