Solve (2k^-1m)(3^-1km^-2)

$$( 2 k ^ { - 1 } m ) ( 3 ^ { - 1 } k m ^ { - 2 } )$$

Evaluate

$$\frac{2}{3m}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$2^{1}\times \frac{1}{k}m^{1}\times \frac{1}{3}k^{1}m^{-2}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times \frac{1}{3}\times \frac{1}{k}k^{1}m^{1}m^{-2}$$

To multiply powers of the same base, add their exponents.

$$2^{1}\times \frac{1}{3}k^{-1+1}m^{1-2}$$

Add the exponents -1 and 1.

$$2^{1}\times \frac{1}{3}k^{0}m^{1-2}$$

For any number a except 0, a^{0}=1.

$$2^{1}\times \frac{1}{3}m^{1-2}$$

Add the exponents 1 and -2.

$$2^{1}\times \frac{1}{3}\times \frac{1}{m}$$

Raise 3 to the power -1.

$$2\times \frac{1}{3}\times \frac{1}{m}$$

Multiply 2 times \frac{1}{3}.

$$\frac{2}{3}\times \frac{1}{m}$$

Differentiate w.r.t. m

$$-\frac{2}{3m^{2}}$$

Steps Using Definition of a Derivative

Multiply k^{-1} and k to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2m\times 3^{-1}m^{-2})$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2m^{-1}\times 3^{-1})$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2m^{-1}\times \frac{1}{3})$$

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{2}{3}m^{-1})$$

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

$$-\frac{2}{3}m^{-1-1}$$

Subtract 1 from -1.

$$-\frac{2}{3}m^{-2}$$