Solve (frac{15n^{5}m^3}{5m^4n^2})^2

$$( \frac { 15 n ^ { 5 } m ^ { 3 } } { 5 m ^ { 4 } n ^ { 2 } } ) ^ { 2 }$$

Evaluate

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

Solution Steps

Cancel out 5n^{2}m^{3} in both numerator and denominator.

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

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

Expand

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

Solution Steps

Cancel out 5n^{2}m^{3} in both numerator and denominator.

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

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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