Solve u^-3*u^7*u^8

$$u ^ { - 3 } \cdot u ^ { 7 } \cdot u ^ { 8 }$$

Evaluate

$$u^{12}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$u^{-3}u^{7}u^{8}$$

Use the Multiplication Rule for Exponents.

$$u^{-3+7+8}$$

Add the exponents -3 and 7.

$$u^{4+8}$$

Add the exponents 4 and 8.

$$u^{12}$$

Differentiate w.r.t. u

$$12u^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and 7 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{4}u^{8})$$

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{12})$$

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

$$12u^{12-1}$$

Subtract 1 from 12.

$$12u^{11}$$