Solve r^-9*r^-6*r^-2

$$r ^ { - 9 } \cdot r ^ { - 6 } \cdot r ^ { - 2 }$$

Evaluate

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

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$r^{-9}r^{-6}r^{-2}$$

Use the Multiplication Rule for Exponents.

$$r^{-9-6-2}$$

Add the exponents -9 and -6.

$$r^{-15-2}$$

Add the exponents -15 and -2.

$$r^{-17}$$

Differentiate w.r.t. r

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -9 and -6 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}r}(r^{-15}r^{-2})$$

To multiply powers of the same base, add their exponents. Add -15 and -2 to get -17.

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

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

$$-17r^{-17-1}$$

Subtract 1 from -17.

$$-17r^{-18}$$