Solve (frac{m^{5}n^4}{m^7n^2})^3

$$( \frac { m ^ { 5 } n ^ { 4 } } { m ^ { 7 } n ^ { 2 } } ) ^ { 3 }$$

Evaluate

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

Solution Steps

Cancel out n^{2}m^{5} in both numerator and denominator.

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

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

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

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

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

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

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

Expand

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

Solution Steps

Cancel out n^{2}m^{5} in both numerator and denominator.

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

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

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

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

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

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

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