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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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