Solve frac{-3*(-2x^{3}y^{2})^{3}}{(-x^1)^4(-4xy^5)^2}

$$\frac { - 3 \times ( - 2 x ^ { 3 } y ^ { 2 } ) ^ { 3 } } { ( - x ^ { 1 } ) ^ { 4 } ( - 4 x y ^ { 5 } ) ^ { 2 } }$$

Evaluate

$$\frac{3x^{3}}{2y^{4}}$$

Short Solution Steps

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

$$\frac{-3\left(-2\right)^{3}\left(x^{3}\right)^{3}\left(y^{2}\right)^{3}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{-3\left(-2\right)^{3}x^{9}\left(y^{2}\right)^{3}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

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

$$\frac{-3\left(-2\right)^{3}x^{9}y^{6}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

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

$$\frac{-3\left(-8\right)x^{9}y^{6}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

Multiply -3 and -8 to get 24.

$$\frac{24x^{9}y^{6}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

Calculate x to the power of 1 and get x.

$$\frac{24x^{9}y^{6}}{\left(-x\right)^{4}\left(-4xy^{5}\right)^{2}}$$

Expand \left(-4xy^{5}\right)^{2}.

$$\frac{24x^{9}y^{6}}{\left(-x\right)^{4}\left(-4\right)^{2}x^{2}\left(y^{5}\right)^{2}}$$

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

$$\frac{24x^{9}y^{6}}{\left(-x\right)^{4}\left(-4\right)^{2}x^{2}y^{10}}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{24x^{9}y^{6}}{\left(-x\right)^{4}\times 16x^{2}y^{10}}$$

Cancel out 8x^{2}y^{6} in both numerator and denominator.

$$\frac{3x^{7}}{2\left(-x\right)^{4}y^{4}}$$

Expand \left(-x\right)^{4}.

$$\frac{3x^{7}}{2\left(-1\right)^{4}x^{4}y^{4}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{3x^{7}}{2\times 1x^{4}y^{4}}$$

Multiply 2 and 1 to get 2.

$$\frac{3x^{7}}{2x^{4}y^{4}}$$

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

$$\frac{3x^{3}}{2y^{4}}$$

Expand

$$\frac{3x^{3}}{2y^{4}}$$

Short Solution Steps

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

$$\frac{-3\left(-2\right)^{3}\left(x^{3}\right)^{3}\left(y^{2}\right)^{3}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{-3\left(-2\right)^{3}x^{9}\left(y^{2}\right)^{3}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

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

$$\frac{-3\left(-2\right)^{3}x^{9}y^{6}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

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

$$\frac{-3\left(-8\right)x^{9}y^{6}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

Multiply -3 and -8 to get 24.

$$\frac{24x^{9}y^{6}}{\left(-x^{1}\right)^{4}\left(-4xy^{5}\right)^{2}}$$

Calculate x to the power of 1 and get x.

$$\frac{24x^{9}y^{6}}{\left(-x\right)^{4}\left(-4xy^{5}\right)^{2}}$$

Expand \left(-4xy^{5}\right)^{2}.

$$\frac{24x^{9}y^{6}}{\left(-x\right)^{4}\left(-4\right)^{2}x^{2}\left(y^{5}\right)^{2}}$$

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

$$\frac{24x^{9}y^{6}}{\left(-x\right)^{4}\left(-4\right)^{2}x^{2}y^{10}}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{24x^{9}y^{6}}{\left(-x\right)^{4}\times 16x^{2}y^{10}}$$

Cancel out 8x^{2}y^{6} in both numerator and denominator.

$$\frac{3x^{7}}{2\left(-x\right)^{4}y^{4}}$$

Expand \left(-x\right)^{4}.

$$\frac{3x^{7}}{2\left(-1\right)^{4}x^{4}y^{4}}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{3x^{7}}{2\times 1x^{4}y^{4}}$$

Multiply 2 and 1 to get 2.

$$\frac{3x^{7}}{2x^{4}y^{4}}$$

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

$$\frac{3x^{3}}{2y^{4}}$$