Solve (3m^{2}n)^{2}*(-2m^2)^3div(-m^2n)^2=

$$( 3 m ^ { 2 } n ) ^ { 2 } \cdot ( - 2 m ^ { 2 } ) ^ { 3 } \div ( - m ^ { 2 } n ) ^ { 2 } =$$

Evaluate

$$-72m^{6}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

$$\frac{9m^{4}n^{2}\left(-2\right)^{3}m^{6}}{\left(\left(-m^{2}\right)n\right)^{2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{9m^{4}n^{2}\left(-8\right)m^{6}}{\left(\left(-m^{2}\right)n\right)^{2}}$$

Multiply 9 and -8 to get -72.

$$\frac{-72m^{4}n^{2}m^{6}}{\left(\left(-m^{2}\right)n\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{-72m^{10}n^{2}}{\left(\left(-m^{2}\right)n\right)^{2}}$$

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

$$\frac{-72m^{10}n^{2}}{\left(-m^{2}\right)^{2}n^{2}}$$

Calculate -m^{2} to the power of 2 and get \left(m^{2}\right)^{2}.

$$\frac{-72m^{10}n^{2}}{\left(m^{2}\right)^{2}n^{2}}$$

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

$$\frac{-72m^{10}}{\left(m^{2}\right)^{2}}$$

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

$$\frac{-72m^{10}}{m^{4}}$$

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

$$-72m^{6}$$

Expand

$$-72m^{6}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 2 and get 9.

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

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

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

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

$$\frac{9m^{4}n^{2}\left(-2\right)^{3}m^{6}}{\left(\left(-m^{2}\right)n\right)^{2}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{9m^{4}n^{2}\left(-8\right)m^{6}}{\left(\left(-m^{2}\right)n\right)^{2}}$$

Multiply 9 and -8 to get -72.

$$\frac{-72m^{4}n^{2}m^{6}}{\left(\left(-m^{2}\right)n\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{-72m^{10}n^{2}}{\left(\left(-m^{2}\right)n\right)^{2}}$$

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

$$\frac{-72m^{10}n^{2}}{\left(-m^{2}\right)^{2}n^{2}}$$

Calculate -m^{2} to the power of 2 and get \left(m^{2}\right)^{2}.

$$\frac{-72m^{10}n^{2}}{\left(m^{2}\right)^{2}n^{2}}$$

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

$$\frac{-72m^{10}}{\left(m^{2}\right)^{2}}$$

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

$$\frac{-72m^{10}}{m^{4}}$$

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

$$-72m^{6}$$