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

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

Evaluate

$$\frac{16m^{4}n^{10}}{9}$$

Solution Steps

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To raise \frac{4m^{2}n^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(4m^{2}n^{5}\right)^{2}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{4^{2}m^{4}n^{10}}{3^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16m^{4}n^{10}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{16m^{4}n^{10}}{9}$$

Expand

$$\frac{16m^{4}n^{10}}{9}$$

Solution Steps

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To raise \frac{4m^{2}n^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(4m^{2}n^{5}\right)^{2}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{4^{2}m^{4}n^{10}}{3^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16m^{4}n^{10}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{16m^{4}n^{10}}{9}$$