Solve (+x^{3}y^{2}z)^{3}:(-x^{6}y^{2}z)+(+2xy^2)*(+3x^2y^2z^2)

$$( + x ^ { 3 } y ^ { 2 } z ) ^ { 3 } : ( - x ^ { 6 } y ^ { 2 } z ) + ( + 2 x y ^ { 2 } ) \cdot ( + 3 x ^ { 2 } y ^ { 2 } z ^ { 2 } )$$

Evaluate

$$5z^{2}x^{3}y^{4}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(x^{3}y^{2}z\right)^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{2}\times 3y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\left(x^{3}y^{2}z\right)^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{4}\times 3z^{2}$$

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

$$\frac{\left(x^{3}\right)^{3}\left(y^{2}\right)^{3}z^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{4}\times 3z^{2}$$

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

$$\frac{x^{9}\left(y^{2}\right)^{3}z^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{4}\times 3z^{2}$$

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

$$\frac{x^{9}y^{6}z^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{4}\times 3z^{2}$$

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

$$\frac{z^{2}y^{4}x^{9}}{-x^{6}}+2x^{3}y^{4}\times 3z^{2}$$

Multiply 2 and 3 to get 6.

$$\frac{z^{2}y^{4}x^{9}}{-x^{6}}+6x^{3}y^{4}z^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{3}y^{4}z^{2} times \frac{-x^{6}}{-x^{6}}.

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

Since \frac{z^{2}y^{4}x^{9}}{-x^{6}} and \frac{6x^{3}y^{4}z^{2}\left(-1\right)x^{6}}{-x^{6}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in z^{2}y^{4}x^{9}+6x^{3}y^{4}z^{2}\left(-1\right)x^{6}.

$$\frac{z^{2}y^{4}x^{9}-6x^{9}y^{4}z^{2}}{-x^{6}}$$

Combine like terms in z^{2}y^{4}x^{9}-6x^{9}y^{4}z^{2}.

$$\frac{-5z^{2}y^{4}x^{9}}{-x^{6}}$$

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

$$\frac{-5z^{2}x^{3}y^{4}}{-1}$$

Anything divided by -1 gives its opposite.

$$5z^{2}x^{3}y^{4}$$

Expand

$$5z^{2}x^{3}y^{4}$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(x^{3}y^{2}z\right)^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{2}\times 3y^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\left(x^{3}y^{2}z\right)^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{4}\times 3z^{2}$$

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

$$\frac{\left(x^{3}\right)^{3}\left(y^{2}\right)^{3}z^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{4}\times 3z^{2}$$

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

$$\frac{x^{9}\left(y^{2}\right)^{3}z^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{4}\times 3z^{2}$$

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

$$\frac{x^{9}y^{6}z^{3}}{\left(-x^{6}\right)y^{2}z}+2x^{3}y^{4}\times 3z^{2}$$

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

$$\frac{z^{2}y^{4}x^{9}}{-x^{6}}+2x^{3}y^{4}\times 3z^{2}$$

Multiply 2 and 3 to get 6.

$$\frac{z^{2}y^{4}x^{9}}{-x^{6}}+6x^{3}y^{4}z^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{3}y^{4}z^{2} times \frac{-x^{6}}{-x^{6}}.

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

Since \frac{z^{2}y^{4}x^{9}}{-x^{6}} and \frac{6x^{3}y^{4}z^{2}\left(-1\right)x^{6}}{-x^{6}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in z^{2}y^{4}x^{9}+6x^{3}y^{4}z^{2}\left(-1\right)x^{6}.

$$\frac{z^{2}y^{4}x^{9}-6x^{9}y^{4}z^{2}}{-x^{6}}$$

Combine like terms in z^{2}y^{4}x^{9}-6x^{9}y^{4}z^{2}.

$$\frac{-5z^{2}y^{4}x^{9}}{-x^{6}}$$

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

$$\frac{-5z^{2}x^{3}y^{4}}{-1}$$

Anything divided by -1 gives its opposite.

$$5z^{2}x^{3}y^{4}$$