Solve {left(m/nright)}^5*{left(n^2/mright)}^4divleft(-mnright)^4

$${ \left( \frac{ m }{ n } \right) }^{ 5 } \times { \left( \frac{ { n }^{ 2 } }{ m } \right) }^{ 4 } \div { \left(-mn \right) }^{ 4 }$$

Evaluate

$$\frac{1}{nm^{3}}$$

Short Solution Steps

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

$$\frac{\frac{m^{5}}{n^{5}}\times \left(\frac{n^{2}}{m}\right)^{4}}{\left(\left(-m\right)n\right)^{4}}$$

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

$$\frac{\frac{m^{5}}{n^{5}}\times \frac{\left(n^{2}\right)^{4}}{m^{4}}}{\left(\left(-m\right)n\right)^{4}}$$

Multiply \frac{m^{5}}{n^{5}} times \frac{\left(n^{2}\right)^{4}}{m^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{m^{5}\left(n^{2}\right)^{4}}{n^{5}m^{4}}}{\left(\left(-m\right)n\right)^{4}}$$

Cancel out m^{4} in both numerator and denominator.

$$\frac{\frac{m\left(n^{2}\right)^{4}}{n^{5}}}{\left(\left(-m\right)n\right)^{4}}$$

Expand \left(\left(-m\right)n\right)^{4}.

$$\frac{\frac{m\left(n^{2}\right)^{4}}{n^{5}}}{\left(-m\right)^{4}n^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{\frac{mn^{8}}{n^{5}}}{\left(-m\right)^{4}n^{4}}$$

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

$$\frac{mn^{3}}{\left(-m\right)^{4}n^{4}}$$

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

$$\frac{m}{n\left(-m\right)^{4}}$$

Expand \left(-m\right)^{4}.

$$\frac{m}{n\left(-1\right)^{4}m^{4}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{m}{n\times 1m^{4}}$$

Cancel out m in both numerator and denominator.

$$\frac{1}{nm^{3}}$$

Expand

$$\frac{1}{nm^{3}}$$

Short Solution Steps

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

$$\frac{\frac{m^{5}}{n^{5}}\times \left(\frac{n^{2}}{m}\right)^{4}}{\left(\left(-m\right)n\right)^{4}}$$

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

$$\frac{\frac{m^{5}}{n^{5}}\times \frac{\left(n^{2}\right)^{4}}{m^{4}}}{\left(\left(-m\right)n\right)^{4}}$$

Multiply \frac{m^{5}}{n^{5}} times \frac{\left(n^{2}\right)^{4}}{m^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{m^{5}\left(n^{2}\right)^{4}}{n^{5}m^{4}}}{\left(\left(-m\right)n\right)^{4}}$$

Cancel out m^{4} in both numerator and denominator.

$$\frac{\frac{m\left(n^{2}\right)^{4}}{n^{5}}}{\left(\left(-m\right)n\right)^{4}}$$

Expand \left(\left(-m\right)n\right)^{4}.

$$\frac{\frac{m\left(n^{2}\right)^{4}}{n^{5}}}{\left(-m\right)^{4}n^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{\frac{mn^{8}}{n^{5}}}{\left(-m\right)^{4}n^{4}}$$

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

$$\frac{mn^{3}}{\left(-m\right)^{4}n^{4}}$$

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

$$\frac{m}{n\left(-m\right)^{4}}$$

Expand \left(-m\right)^{4}.

$$\frac{m}{n\left(-1\right)^{4}m^{4}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{m}{n\times 1m^{4}}$$

Cancel out m in both numerator and denominator.

$$\frac{1}{nm^{3}}$$