Solve (-2xy)*(-x^2y)^2*(-6xz)

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

Evaluate

$$12zy^{3}x^{6}$$

Solution Steps

Multiply x and x to get x^{2}.

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

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

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

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

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

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

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

Multiply -2 and -6 to get 12.

$$12x^{2}y^{3}\left(x^{2}\right)^{2}z$$

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

$$12x^{2}y^{3}x^{4}z$$

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

$$12x^{6}y^{3}z$$

Expand

$$12zy^{3}x^{6}$$

Solution Steps

Multiply x and x to get x^{2}.

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

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

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

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

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

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

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

Multiply -2 and -6 to get 12.

$$12x^{2}y^{3}\left(x^{2}\right)^{2}z$$

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

$$12x^{2}y^{3}x^{4}z$$

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

$$12x^{6}y^{3}z$$