Solve u^2u^-6u

$$u ^ { 2 } u ^ { - 6 } u$$

Evaluate

$$\frac{1}{u^{3}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$u^{2}u^{-6}u^{1}$$

Use the Multiplication Rule for Exponents.

$$u^{2-6+1}$$

Add the exponents 2 and -6.

$$u^{-4+1}$$

Add the exponents -4 and 1.

$$u^{-3}$$

Differentiate w.r.t. u

$$-\frac{3}{u^{4}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and -6 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{-4}u)$$

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{-3})$$

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

$$-3u^{-3-1}$$

Subtract 1 from -3.

$$-3u^{-4}$$