Solve (-1/3mn^{3})*6m^2n+5m^3n^2*2/5n^2

$$( - \frac { 1 } { 3 } m n ^ { 3 } ) \cdot 6 m ^ { 2 } n + 5 m ^ { 3 } n ^ { 2 } \cdot \frac { 2 } { 5 } n ^ { 2 }$$

Evaluate

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Solution Steps

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

$$-\frac{1}{3}m^{3}n^{3}\times 6n+5m^{3}n^{2}\times \frac{2}{5}n^{2}$$

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

$$-\frac{1}{3}m^{3}n^{4}\times 6+5m^{3}n^{2}\times \frac{2}{5}n^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-\frac{1}{3}m^{3}n^{4}\times 6+5m^{3}n^{4}\times \frac{2}{5}$$

Multiply -\frac{1}{3} and 6 to get -2.

$$-2m^{3}n^{4}+5m^{3}n^{4}\times \frac{2}{5}$$

Multiply 5 and \frac{2}{5} to get 2.

$$-2m^{3}n^{4}+2m^{3}n^{4}$$

Combine -2m^{3}n^{4} and 2m^{3}n^{4} to get 0.

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Factor

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Solution Steps

Factor out 2.

$$2\left(-mn^{3}m^{2}n+m^{3}n^{2}n^{2}\right)$$

Consider -m^{3}n^{4}+m^{3}n^{4}. Factor out m^{3}n^{4}.

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