Solve (4a^2)(5a^-3)(3/10a^15)

$$( 4 a ^ { 2 } ) ( 5 a ^ { - 3 } ) ( \frac { 3 } { 10 } a ^ { 15 } )$$

Evaluate

$$6a^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$4a^{-1}\times 5\times \frac{3}{10}a^{15}$$

To multiply powers of the same base, add their exponents. Add -1 and 15 to get 14.

$$4a^{14}\times 5\times \frac{3}{10}$$

Multiply 4 and 5 to get 20.

$$20a^{14}\times \frac{3}{10}$$

Multiply 20 and \frac{3}{10} to get 6.

$$6a^{14}$$

Differentiate w.r.t. a

$$84a^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{-1}\times 5\times \frac{3}{10}a^{15})$$

To multiply powers of the same base, add their exponents. Add -1 and 15 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{14}\times 5\times \frac{3}{10})$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20a^{14}\times \frac{3}{10})$$

Multiply 20 and \frac{3}{10} to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{14})$$

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

$$14\times 6a^{14-1}$$

Multiply 14 times 6.

$$84a^{14-1}$$

Subtract 1 from 14.

$$84a^{13}$$