Solve (-2x^{2}y)^{3}+(3x^2)^2(-x^2)(-y^3)=

$$( - 2 x ^ { 2 } y ) ^ { 3 } + ( 3 x ^ { 2 } ) ^ { 2 } ( - x ^ { 2 } ) ( - y ^ { 3 } ) =$$

Evaluate

$$y^{3}x^{6}$$

Solution Steps

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

$$\left(-2\right)^{3}\left(x^{2}\right)^{3}y^{3}+\left(3x^{2}\right)^{2}\left(-x^{2}\right)\left(-y^{3}\right)$$

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

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

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

$$-8x^{6}y^{3}+\left(3x^{2}\right)^{2}\left(-x^{2}\right)\left(-y^{3}\right)$$

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

$$-8x^{6}y^{3}+3^{2}\left(x^{2}\right)^{2}\left(-x^{2}\right)\left(-y^{3}\right)$$

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

$$-8x^{6}y^{3}+3^{2}x^{4}\left(-x^{2}\right)\left(-y^{3}\right)$$

Calculate 3 to the power of 2 and get 9.

$$-8x^{6}y^{3}+9x^{4}\left(-x^{2}\right)\left(-y^{3}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-8x^{6}y^{3}+9x^{6}\left(-1\right)\left(-1\right)y^{3}$$

Multiply 9 and -1 to get -9.

$$-8x^{6}y^{3}-9x^{6}\left(-1\right)y^{3}$$

Multiply -9 and -1 to get 9.

$$-8x^{6}y^{3}+9x^{6}y^{3}$$

Combine -8x^{6}y^{3} and 9x^{6}y^{3} to get x^{6}y^{3}.

$$x^{6}y^{3}$$

Expand

$$y^{3}x^{6}$$

Solution Steps

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

$$\left(-2\right)^{3}\left(x^{2}\right)^{3}y^{3}+\left(3x^{2}\right)^{2}\left(-x^{2}\right)\left(-y^{3}\right)$$

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

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

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

$$-8x^{6}y^{3}+\left(3x^{2}\right)^{2}\left(-x^{2}\right)\left(-y^{3}\right)$$

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

$$-8x^{6}y^{3}+3^{2}\left(x^{2}\right)^{2}\left(-x^{2}\right)\left(-y^{3}\right)$$

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

$$-8x^{6}y^{3}+3^{2}x^{4}\left(-x^{2}\right)\left(-y^{3}\right)$$

Calculate 3 to the power of 2 and get 9.

$$-8x^{6}y^{3}+9x^{4}\left(-x^{2}\right)\left(-y^{3}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-8x^{6}y^{3}+9x^{6}\left(-1\right)\left(-1\right)y^{3}$$

Multiply 9 and -1 to get -9.

$$-8x^{6}y^{3}-9x^{6}\left(-1\right)y^{3}$$

Multiply -9 and -1 to get 9.

$$-8x^{6}y^{3}+9x^{6}y^{3}$$

Combine -8x^{6}y^{3} and 9x^{6}y^{3} to get x^{6}y^{3}.

$$x^{6}y^{3}$$