Solve (2m^2/3n^9)^2

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

Evaluate

$$\frac{4m^{4}}{9n^{18}}$$

Solution Steps

To raise \frac{2m^{2}}{3n^{9}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Expand \left(3n^{9}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{4m^{4}}{3^{2}n^{18}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4m^{4}}{9n^{18}}$$

Expand

$$\frac{4m^{4}}{9n^{18}}$$

Solution Steps

To raise \frac{2m^{2}}{3n^{9}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Expand \left(3n^{9}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\frac{4m^{4}}{3^{2}n^{18}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4m^{4}}{9n^{18}}$$