Solve (5m^{6}n^3)(6m^4p^4)(1/3mp^5)

$$( 5 m ^ { 6 } n ^ { 3 } ) ( 6 m ^ { 4 } p ^ { 4 } ) ( \frac { 1 } { 3 } m p ^ { 5 } )$$

Evaluate

$$10n^{3}p^{9}m^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$5m^{10}n^{3}\times 6p^{4}\times \frac{1}{3}mp^{5}$$

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$5m^{11}n^{3}\times 6p^{4}\times \frac{1}{3}p^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$5m^{11}n^{3}\times 6p^{9}\times \frac{1}{3}$$

Multiply 5 and 6 to get 30.

$$30m^{11}n^{3}p^{9}\times \frac{1}{3}$$

Multiply 30 and \frac{1}{3} to get 10.

$$10m^{11}n^{3}p^{9}$$

Differentiate w.r.t. n

$$30n^{2}p^{9}m^{11}$$