Solve x^-5*x^-7*x^-9

$$x ^ { - 5 } \cdot x ^ { - 7 } \cdot x ^ { - 9 }$$

Evaluate

$$\frac{1}{x^{21}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{-5}x^{-7}x^{-9}$$

Use the Multiplication Rule for Exponents.

$$x^{-5-7-9}$$

Add the exponents -5 and -7.

$$x^{-12-9}$$

Add the exponents -12 and -9.

$$x^{-21}$$

Differentiate w.r.t. x

$$-\frac{21}{x^{22}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -5 and -7 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-12}x^{-9})$$

To multiply powers of the same base, add their exponents. Add -12 and -9 to get -21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-21})$$

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

$$-21x^{-21-1}$$

Subtract 1 from -21.

$$-21x^{-22}$$