Solve (24m^-2n)(1/4mn)

$$( 24 m ^ { - 2 } n ) ( \frac { 1 } { 4 } m n )$$

Evaluate

$$\frac{6n^{2}}{m}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$24^{1}m^{-2}n^{1}\times \left(\frac{1}{4}\right)^{1}m^{1}n^{1}$$

Use the Commutative Property of Multiplication.

$$24^{1}\times \left(\frac{1}{4}\right)^{1}m^{-2}m^{1}n^{1}n^{1}$$

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

$$24^{1}\times \left(\frac{1}{4}\right)^{1}m^{-2+1}n^{1+1}$$

Add the exponents -2 and 1.

$$24^{1}\times \left(\frac{1}{4}\right)^{1}\times \frac{1}{m}n^{1+1}$$

Add the exponents 1 and 1.

$$24^{1}\times \left(\frac{1}{4}\right)^{1}\times \frac{1}{m}n^{2}$$

Multiply 24 times \frac{1}{4}.

$$6\times \frac{1}{m}n^{2}$$

Differentiate w.r.t. m

$$-6\times \left(\frac{n}{m}\right)^{2}$$