Solve (3a^5)(2/6a^-3)

$$( 3 a ^ { 5 } ) ( \frac { 2 } { 6 } a ^ { - 3 } )$$

Evaluate

$$a^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -3 to get 2.

$$3a^{2}\times \frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Multiply 3 and \frac{1}{3} to get 1.

$$a^{2}$$

Differentiate w.r.t. a

$$2a$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and -3 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{2}\times \frac{2}{6})$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Multiply 3 and \frac{1}{3} to get 1.

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

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

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

Subtract 1 from 2.

$$2a^{1}$$

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

$$2a$$