Solve (x^-4)(x^-7)(x^5)

$$( x ^ { - 4 } ) ( x ^ { - 7 } ) ( x ^ { 5 } )$$

Evaluate

$$\frac{1}{x^{6}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{-4}x^{-7}x^{5}$$

Use the Multiplication Rule for Exponents.

$$x^{-4-7+5}$$

Add the exponents -4 and -7.

$$x^{-11+5}$$

Add the exponents -11 and 5.

$$x^{-6}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -4 and -7 to get -11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-11}x^{5})$$

To multiply powers of the same base, add their exponents. Add -11 and 5 to get -6.

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

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

$$-6x^{-6-1}$$

Subtract 1 from -6.

$$-6x^{-7}$$