Solve left(-x^2yright)^3left(-2x^3yright)^2

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

Evaluate

$$-4y^{5}x^{12}$$

Solution Steps

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(-x^{2}\right)^{3}y^{5}\times 4x^{6}$$

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

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

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

$$\left(-1\right)^{3}x^{6}y^{5}\times 4x^{6}$$

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

$$-x^{6}y^{5}\times 4x^{6}$$

Multiply -1 and 4 to get -4.

$$-4x^{6}y^{5}x^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-4x^{12}y^{5}$$

Expand

$$-4y^{5}x^{12}$$

Solution Steps

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(-x^{2}\right)^{3}y^{5}\times 4x^{6}$$

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

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

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

$$\left(-1\right)^{3}x^{6}y^{5}\times 4x^{6}$$

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

$$-x^{6}y^{5}\times 4x^{6}$$

Multiply -1 and 4 to get -4.

$$-4x^{6}y^{5}x^{6}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-4x^{12}y^{5}$$