Solve (-m^{2}n)^3div(6m^6n^3)*(-12mn^2)

$$( - m ^ { 2 } n ) ^ { 3 } \div ( 6 m ^ { 6 } n ^ { 3 } ) \cdot ( - 12 m n ^ { 2 } )$$

Evaluate

$$2mn^{2}$$

Short Solution Steps

Expand \left(\left(-m^{2}\right)n\right)^{3}.

$$\frac{\left(-m^{2}\right)^{3}n^{3}}{6m^{6}n^{3}}\left(-12\right)mn^{2}$$

Cancel out n^{3} in both numerator and denominator.

$$\frac{\left(-m^{2}\right)^{3}}{6m^{6}}\left(-12\right)mn^{2}$$

Express \frac{\left(-m^{2}\right)^{3}}{6m^{6}}\left(-12\right) as a single fraction.

$$\frac{-\left(-m^{2}\right)^{3}\times 12}{6m^{6}}mn^{2}$$

Cancel out 6 in both numerator and denominator.

$$\frac{-2\left(-m^{2}\right)^{3}}{m^{6}}mn^{2}$$

Express \frac{-2\left(-m^{2}\right)^{3}}{m^{6}}m as a single fraction.

$$\frac{-2\left(-m^{2}\right)^{3}m}{m^{6}}n^{2}$$

Cancel out m in both numerator and denominator.

$$\frac{-2\left(-m^{2}\right)^{3}}{m^{5}}n^{2}$$

Express \frac{-2\left(-m^{2}\right)^{3}}{m^{5}}n^{2} as a single fraction.

$$\frac{-2\left(-m^{2}\right)^{3}n^{2}}{m^{5}}$$

Expand \left(-m^{2}\right)^{3}.

$$\frac{-2\left(-1\right)^{3}\left(m^{2}\right)^{3}n^{2}}{m^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

Calculate -1 to the power of 3 and get -1.

$$\frac{-2\left(-1\right)m^{6}n^{2}}{m^{5}}$$

Multiply -2 and -1 to get 2.

$$\frac{2m^{6}n^{2}}{m^{5}}$$

Cancel out m^{5} in both numerator and denominator.

$$2mn^{2}$$

Expand

$$2mn^{2}$$

Short Solution Steps

Expand \left(\left(-m^{2}\right)n\right)^{3}.

$$\frac{\left(-m^{2}\right)^{3}n^{3}}{6m^{6}n^{3}}\left(-12\right)mn^{2}$$

Cancel out n^{3} in both numerator and denominator.

$$\frac{\left(-m^{2}\right)^{3}}{6m^{6}}\left(-12\right)mn^{2}$$

Express \frac{\left(-m^{2}\right)^{3}}{6m^{6}}\left(-12\right) as a single fraction.

$$\frac{-\left(-m^{2}\right)^{3}\times 12}{6m^{6}}mn^{2}$$

Cancel out 6 in both numerator and denominator.

$$\frac{-2\left(-m^{2}\right)^{3}}{m^{6}}mn^{2}$$

Express \frac{-2\left(-m^{2}\right)^{3}}{m^{6}}m as a single fraction.

$$\frac{-2\left(-m^{2}\right)^{3}m}{m^{6}}n^{2}$$

Cancel out m in both numerator and denominator.

$$\frac{-2\left(-m^{2}\right)^{3}}{m^{5}}n^{2}$$

Express \frac{-2\left(-m^{2}\right)^{3}}{m^{5}}n^{2} as a single fraction.

$$\frac{-2\left(-m^{2}\right)^{3}n^{2}}{m^{5}}$$

Expand \left(-m^{2}\right)^{3}.

$$\frac{-2\left(-1\right)^{3}\left(m^{2}\right)^{3}n^{2}}{m^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

Calculate -1 to the power of 3 and get -1.

$$\frac{-2\left(-1\right)m^{6}n^{2}}{m^{5}}$$

Multiply -2 and -1 to get 2.

$$\frac{2m^{6}n^{2}}{m^{5}}$$

Cancel out m^{5} in both numerator and denominator.

$$2mn^{2}$$