Solve (4m^2)(3n^5)/(2m^-3)(-mn)^3=

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

Evaluate

$$-6\left(mn\right)^{2}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

Multiply 2 and 3 to get 6.

$$\frac{6m^{5}n^{5}}{\left(\left(-m\right)n\right)^{3}}$$

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

$$\frac{6m^{5}n^{5}}{\left(-m\right)^{3}n^{3}}$$

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

$$\frac{6n^{2}m^{5}}{\left(-m\right)^{3}}$$

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

$$\frac{6n^{2}m^{5}}{\left(-1\right)^{3}m^{3}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{6n^{2}m^{5}}{-m^{3}}$$

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

$$\frac{6m^{2}n^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$-6m^{2}n^{2}$$

Expand

$$-6\left(mn\right)^{2}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

Multiply 2 and 3 to get 6.

$$\frac{6m^{5}n^{5}}{\left(\left(-m\right)n\right)^{3}}$$

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

$$\frac{6m^{5}n^{5}}{\left(-m\right)^{3}n^{3}}$$

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

$$\frac{6n^{2}m^{5}}{\left(-m\right)^{3}}$$

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

$$\frac{6n^{2}m^{5}}{\left(-1\right)^{3}m^{3}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{6n^{2}m^{5}}{-m^{3}}$$

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

$$\frac{6m^{2}n^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$-6m^{2}n^{2}$$