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

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

Evaluate

$$\frac{1}{n^{6}m^{8}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\left(\frac{2m^{2}n^{3}p^{4}}{\left(-p\right)m^{6}n^{2}\left(-2\right)n^{4}p^{3}}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\left(\frac{2m^{2}n^{3}p^{4}}{\left(-p\right)m^{6}n^{6}\left(-2\right)p^{3}}\right)^{2}$$

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

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

Multiply -1 and -1 to get 1.

$$\left(\frac{p}{pn^{3}m^{4}}\right)^{2}$$

Cancel out p in both numerator and denominator.

$$\left(\frac{1}{n^{3}m^{4}}\right)^{2}$$

To raise \frac{1}{n^{3}m^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{2}}{\left(n^{3}m^{4}\right)^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{\left(n^{3}m^{4}\right)^{2}}$$

Expand \left(n^{3}m^{4}\right)^{2}.

$$\frac{1}{\left(n^{3}\right)^{2}\left(m^{4}\right)^{2}}$$

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

$$\frac{1}{n^{6}\left(m^{4}\right)^{2}}$$

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

$$\frac{1}{n^{6}m^{8}}$$

Expand

$$\frac{1}{n^{6}m^{8}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\left(\frac{2m^{2}n^{3}p^{4}}{\left(-p\right)m^{6}n^{2}\left(-2\right)n^{4}p^{3}}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\left(\frac{2m^{2}n^{3}p^{4}}{\left(-p\right)m^{6}n^{6}\left(-2\right)p^{3}}\right)^{2}$$

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

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

Multiply -1 and -1 to get 1.

$$\left(\frac{p}{pn^{3}m^{4}}\right)^{2}$$

Cancel out p in both numerator and denominator.

$$\left(\frac{1}{n^{3}m^{4}}\right)^{2}$$

To raise \frac{1}{n^{3}m^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{2}}{\left(n^{3}m^{4}\right)^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{\left(n^{3}m^{4}\right)^{2}}$$

Expand \left(n^{3}m^{4}\right)^{2}.

$$\frac{1}{\left(n^{3}\right)^{2}\left(m^{4}\right)^{2}}$$

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

$$\frac{1}{n^{6}\left(m^{4}\right)^{2}}$$

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

$$\frac{1}{n^{6}m^{8}}$$