Solve (16b^2)(9b^5)

$$( 16 b ^ { 2 } ) ( 9 b ^ { 5 } )$$

Evaluate

$$144b^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$16b^{7}\times 9$$

Multiply 16 and 9 to get 144.

$$144b^{7}$$

Differentiate w.r.t. b

$$1008b^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}b}(16b^{7}\times 9)$$

Multiply 16 and 9 to get 144.

$$\frac{\mathrm{d}}{\mathrm{d}b}(144b^{7})$$

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

$$7\times 144b^{7-1}$$

Multiply 7 times 144.

$$1008b^{7-1}$$

Subtract 1 from 7.

$$1008b^{6}$$