Solve 27a^frac{1{2}}3a^frac{3{2}}

$$27 a ^ { \frac { 1 } { 2 } } 3 a ^ { \frac { 3 } { 2 } }$$

Evaluate

$$81a^{2}$$

Solution Steps

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

$$27a^{2}\times 3$$

Multiply 27 and 3 to get 81.

$$81a^{2}$$

Differentiate w.r.t. a

$$162a$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(27a^{2}\times 3)$$

Multiply 27 and 3 to get 81.

$$\frac{\mathrm{d}}{\mathrm{d}a}(81a^{2})$$

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

$$2\times 81a^{2-1}$$

Multiply 2 times 81.

$$162a^{2-1}$$

Subtract 1 from 2.

$$162a^{1}$$

For any term t, t^{1}=t.

$$162a$$