Solve (-5b^3)(-3b^6)

$$( - 5 b ^ { 3 } ) ( - 3 b ^ { 6 } )$$

Evaluate

$$15b^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$-5b^{9}\left(-3\right)$$

Multiply -5 and -3 to get 15.

$$15b^{9}$$

Differentiate w.r.t. b

$$135b^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-5b^{9}\left(-3\right))$$

Multiply -5 and -3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}b}(15b^{9})$$

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

$$9\times 15b^{9-1}$$

Multiply 9 times 15.

$$135b^{9-1}$$

Subtract 1 from 9.

$$135b^{8}$$