Solve (-k^{-4}m^7)(3k^5m^-1)(2k^-2m)

$$( - k ^ { - 4 } m ^ { 7 } ) ( 3 k ^ { 5 } m ^ { - 1 } ) ( 2 k ^ { - 2 } m )$$

Evaluate

$$-\frac{6m^{7}}{k}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and -1 to get 6.

$$\left(-k^{-4}\right)m^{6}\times 3k^{5}\times 2k^{-2}m$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\left(-k^{-4}\right)m^{7}\times 3k^{5}\times 2k^{-2}$$

To multiply powers of the same base, add their exponents. Add 5 and -2 to get 3.

$$\left(-k^{-4}\right)m^{7}\times 3k^{3}\times 2$$

Multiply 3 and 2 to get 6.

$$\left(-k^{-4}\right)m^{7}\times 6k^{3}$$

Multiply -1 and 6 to get -6.

$$-6k^{-4}m^{7}k^{3}$$

To multiply powers of the same base, add their exponents. Add -4 and 3 to get -1.

$$-6k^{-1}m^{7}$$

Differentiate w.r.t. m

$$-\frac{42m^{6}}{k}$$