Solve left(-x^2yright)^3left(-2xy^2right)^24xz

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

Evaluate

$$-16zy^{7}x^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

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

Multiply 4 and 4 to get 16.

$$\left(-x^{2}\right)^{3}y^{7}\times 16x^{2}xz$$

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

$$\left(-x^{2}\right)^{3}y^{7}\times 16x^{3}z$$

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

$$\left(-1\right)^{3}\left(x^{2}\right)^{3}y^{7}\times 16x^{3}z$$

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

$$\left(-1\right)^{3}x^{6}y^{7}\times 16x^{3}z$$

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

$$-x^{6}y^{7}\times 16x^{3}z$$

Multiply -1 and 16 to get -16.

$$-16x^{6}y^{7}x^{3}z$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-16x^{9}y^{7}z$$

Expand

$$-16zy^{7}x^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

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

Multiply 4 and 4 to get 16.

$$\left(-x^{2}\right)^{3}y^{7}\times 16x^{2}xz$$

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

$$\left(-x^{2}\right)^{3}y^{7}\times 16x^{3}z$$

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

$$\left(-1\right)^{3}\left(x^{2}\right)^{3}y^{7}\times 16x^{3}z$$

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

$$\left(-1\right)^{3}x^{6}y^{7}\times 16x^{3}z$$

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

$$-x^{6}y^{7}\times 16x^{3}z$$

Multiply -1 and 16 to get -16.

$$-16x^{6}y^{7}x^{3}z$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-16x^{9}y^{7}z$$