Solve (3n^3/4m^2n^6)^2

$$( \frac { 3 n ^ { 3 } } { 4 m ^ { 2 } n ^ { 6 } } ) ^ { 2 }$$

Evaluate

$$\frac{9}{16m^{4}n^{6}}$$

Solution Steps

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

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

To raise \frac{3}{4m^{2}n^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{\left(4m^{2}n^{3}\right)^{2}}$$

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

$$\frac{9}{4^{2}\left(m^{2}\right)^{2}\left(n^{3}\right)^{2}}$$

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

$$\frac{9}{4^{2}m^{4}\left(n^{3}\right)^{2}}$$

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

$$\frac{9}{4^{2}m^{4}n^{6}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9}{16m^{4}n^{6}}$$

Expand

$$\frac{9}{16m^{4}n^{6}}$$

Solution Steps

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

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

To raise \frac{3}{4m^{2}n^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{\left(4m^{2}n^{3}\right)^{2}}$$

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

$$\frac{9}{4^{2}\left(m^{2}\right)^{2}\left(n^{3}\right)^{2}}$$

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

$$\frac{9}{4^{2}m^{4}\left(n^{3}\right)^{2}}$$

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

$$\frac{9}{4^{2}m^{4}n^{6}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9}{16m^{4}n^{6}}$$