Solve (frac{3m^{3}n^3p^3}{2p^3})^2

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

Evaluate

$$\frac{9\left(mn\right)^{6}}{4}$$

Solution Steps

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

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

To raise \frac{3m^{3}n^{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

$$\frac{3^{2}m^{6}n^{6}}{2^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9m^{6}n^{6}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{9m^{6}n^{6}}{4}$$

Expand

$$\frac{9\left(mn\right)^{6}}{4}$$

Solution Steps

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

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

To raise \frac{3m^{3}n^{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

$$\frac{3^{2}m^{6}n^{6}}{2^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9m^{6}n^{6}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{9m^{6}n^{6}}{4}$$