Solve m^11*m^-3*m

$$m ^ { 11 } \times m ^ { - 3 } \times m$$

Evaluate

$$m^{9}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$m^{11}m^{-3}m^{1}$$

Use the Multiplication Rule for Exponents.

$$m^{11-3+1}$$

Add the exponents 11 and -3.

$$m^{8+1}$$

Add the exponents 8 and 1.

$$m^{9}$$

Differentiate w.r.t. m

$$9m^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 11 and -3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{8}m)$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{9})$$

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

$$9m^{9-1}$$

Subtract 1 from 9.

$$9m^{8}$$