Solve (frac{-2m^{2}n^3}{m^2n^4})^3

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

Evaluate

$$-\frac{8}{n^{3}}$$

Solution Steps

Cancel out m^{2}n^{3} in both numerator and denominator.

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

To raise \frac{-2}{n} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate -2 to the power of 3 and get -8.

$$\frac{-8}{n^{3}}$$

Expand

$$-\frac{8}{n^{3}}$$

Solution Steps

Cancel out m^{2}n^{3} in both numerator and denominator.

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

To raise \frac{-2}{n} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate -2 to the power of 3 and get -8.

$$\frac{-8}{n^{3}}$$