Solve (5m^2/n)^3

$$( \frac { 5 m ^ { 2 } } { n } ) ^ { 3 }$$

Evaluate

$$\frac{125m^{6}}{n^{3}}$$

Solution Steps

To raise \frac{5m^{2}}{n} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5m^{2}\right)^{3}}{n^{3}}$$

Expand \left(5m^{2}\right)^{3}.

$$\frac{5^{3}\left(m^{2}\right)^{3}}{n^{3}}$$

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

$$\frac{5^{3}m^{6}}{n^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125m^{6}}{n^{3}}$$

Expand

$$\frac{125m^{6}}{n^{3}}$$

Solution Steps

To raise \frac{5m^{2}}{n} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5m^{2}\right)^{3}}{n^{3}}$$

Expand \left(5m^{2}\right)^{3}.

$$\frac{5^{3}\left(m^{2}\right)^{3}}{n^{3}}$$

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

$$\frac{5^{3}m^{6}}{n^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125m^{6}}{n^{3}}$$