Solve (-3m^{2}n^3)^2div(0.5m^4n)div(3n)^3

$$( - 3 m ^ { 2 } n ^ { 3 } ) ^ { 2 } \div ( 0.5 m ^ { 4 } n ) \div ( 3 n ) ^ { 3 }$$

Evaluate

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

Solution Steps

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

$$\frac{\frac{\left(-3\right)^{2}\left(m^{2}\right)^{2}\left(n^{3}\right)^{2}}{0.5m^{4}n}}{\left(3n\right)^{3}}$$

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

$$\frac{\frac{\left(-3\right)^{2}m^{4}\left(n^{3}\right)^{2}}{0.5m^{4}n}}{\left(3n\right)^{3}}$$

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

$$\frac{\frac{\left(-3\right)^{2}m^{4}n^{6}}{0.5m^{4}n}}{\left(3n\right)^{3}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{\frac{9m^{4}n^{6}}{0.5m^{4}n}}{\left(3n\right)^{3}}$$

Cancel out nm^{4} in both numerator and denominator.

$$\frac{\frac{9n^{5}}{0.5}}{\left(3n\right)^{3}}$$

Divide 9n^{5} by 0.5 to get 18n^{5}.

$$\frac{18n^{5}}{\left(3n\right)^{3}}$$

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

$$\frac{18n^{5}}{3^{3}n^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{18n^{5}}{27n^{3}}$$

Cancel out 9n^{3} in both numerator and denominator.

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

Expand

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

Solution Steps

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

$$\frac{\frac{\left(-3\right)^{2}\left(m^{2}\right)^{2}\left(n^{3}\right)^{2}}{0.5m^{4}n}}{\left(3n\right)^{3}}$$

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

$$\frac{\frac{\left(-3\right)^{2}m^{4}\left(n^{3}\right)^{2}}{0.5m^{4}n}}{\left(3n\right)^{3}}$$

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

$$\frac{\frac{\left(-3\right)^{2}m^{4}n^{6}}{0.5m^{4}n}}{\left(3n\right)^{3}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{\frac{9m^{4}n^{6}}{0.5m^{4}n}}{\left(3n\right)^{3}}$$

Cancel out nm^{4} in both numerator and denominator.

$$\frac{\frac{9n^{5}}{0.5}}{\left(3n\right)^{3}}$$

Divide 9n^{5} by 0.5 to get 18n^{5}.

$$\frac{18n^{5}}{\left(3n\right)^{3}}$$

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

$$\frac{18n^{5}}{3^{3}n^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{18n^{5}}{27n^{3}}$$

Cancel out 9n^{3} in both numerator and denominator.

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