Solve b^-3*b^-8*b^-6

$$b ^ { - 3 } \cdot b ^ { - 8 } \cdot b ^ { - 6 }$$

Evaluate

$$\frac{1}{b^{17}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$b^{-3}b^{-8}b^{-6}$$

Use the Multiplication Rule for Exponents.

$$b^{-3-8-6}$$

Add the exponents -3 and -8.

$$b^{-11-6}$$

Add the exponents -11 and -6.

$$b^{-17}$$

Differentiate w.r.t. b

$$-\frac{17}{b^{18}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and -8 to get -11.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{-11}b^{-6})$$

To multiply powers of the same base, add their exponents. Add -11 and -6 to get -17.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{-17})$$

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

$$-17b^{-17-1}$$

Subtract 1 from -17.

$$-17b^{-18}$$