Solve (-4^2m^3n/n^2)^-2

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

Evaluate

$$\frac{n^{2}}{256m^{6}}$$

Solution Steps

Cancel out n in both numerator and denominator.

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

Calculate 4 to the power of 2 and get 16.

$$\left(\frac{-16m^{3}}{n}\right)^{-2}$$

To raise \frac{-16m^{3}}{n} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-16m^{3}\right)^{-2}}{n^{-2}}$$

Expand \left(-16m^{3}\right)^{-2}.

$$\frac{\left(-16\right)^{-2}\left(m^{3}\right)^{-2}}{n^{-2}}$$

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

$$\frac{\left(-16\right)^{-2}m^{-6}}{n^{-2}}$$

Calculate -16 to the power of -2 and get \frac{1}{256}.

$$\frac{\frac{1}{256}m^{-6}}{n^{-2}}$$

Expand

$$\frac{n^{2}}{256m^{6}}$$

Solution Steps

Cancel out n in both numerator and denominator.

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

Calculate 4 to the power of 2 and get 16.

$$\left(\frac{-16m^{3}}{n}\right)^{-2}$$

To raise \frac{-16m^{3}}{n} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-16m^{3}\right)^{-2}}{n^{-2}}$$

Expand \left(-16m^{3}\right)^{-2}.

$$\frac{\left(-16\right)^{-2}\left(m^{3}\right)^{-2}}{n^{-2}}$$

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

$$\frac{\left(-16\right)^{-2}m^{-6}}{n^{-2}}$$

Calculate -16 to the power of -2 and get \frac{1}{256}.

$$\frac{\frac{1}{256}m^{-6}}{n^{-2}}$$