Solve (5m^2n)(2m^-3n)(m^-4)

$$( 5 m ^ { 2 } n ) ( 2 m ^ { - 3 } n ) ( m ^ { - 4 } )$$

Evaluate

$$\frac{10n^{2}}{m^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$5m^{-1}n\times 2nm^{-4}$$

To multiply powers of the same base, add their exponents. Add -1 and -4 to get -5.

$$5m^{-5}n\times 2n$$

Multiply n and n to get n^{2}.

$$5m^{-5}n^{2}\times 2$$

Multiply 5 and 2 to get 10.

$$10m^{-5}n^{2}$$

Differentiate w.r.t. m

$$-\frac{50n^{2}}{m^{6}}$$