Solve (-2b^2)*(-7b^3)=

$$( - 2 b ^ { 2 } ) \cdot ( - 7 b ^ { 3 } ) =$$

Evaluate

$$14b^{5}$$

Solution Steps

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

$$-2b^{5}\left(-7\right)$$

Multiply -2 and -7 to get 14.

$$14b^{5}$$

Differentiate w.r.t. b

$$70b^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(-2b^{5}\left(-7\right))$$

Multiply -2 and -7 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}b}(14b^{5})$$

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

$$5\times 14b^{5-1}$$

Multiply 5 times 14.

$$70b^{5-1}$$

Subtract 1 from 5.

$$70b^{4}$$