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

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

Evaluate

$$6a$$

Solution Steps

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

$$3a^{1}\times 2$$

Calculate a to the power of 1 and get a.

$$3a\times 2$$

Multiply 3 and 2 to get 6.

$$6a$$

Differentiate w.r.t. a

$$6$$

Steps Using Definition of a Derivative

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

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

Calculate a to the power of 1 and get a.

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

Multiply 3 and 2 to get 6.

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

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

$$6a^{1-1}$$

Subtract 1 from 1.

$$6a^{0}$$

For any term t except 0, t^{0}=1.

$$6\times 1$$

For any term t, t\times 1=t and 1t=t.

$$6$$