Solve (2b^-3)(-3b^-4)

$$( 2 b ^ { - 3 } ) ( - 3 b ^ { - 4 } )$$

Evaluate

$$-\frac{6}{b^{7}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -4 to get -7.

$$2b^{-7}\left(-3\right)$$

Multiply 2 and -3 to get -6.

$$-6b^{-7}$$

Differentiate w.r.t. b

$$\frac{42}{b^{8}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and -4 to get -7.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{-7}\left(-3\right))$$

Multiply 2 and -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-6b^{-7})$$

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

$$-7\left(-6\right)b^{-7-1}$$

Multiply -7 times -6.

$$42b^{-7-1}$$

Subtract 1 from -7.

$$42b^{-8}$$