Solve (-3x^2y)^2*(-2/3xyz)*xz^2

$$( - 3 x ^ { 2 } y ) ^ { 2 } \cdot ( - \frac { 2 } { 3 } x y z ) \cdot x z ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Calculate -3 to the power of 2 and get 9.

$$9x^{4}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}$$

Multiply 9 and -\frac{2}{3} to get -6.

$$-6x^{4}y^{2}x^{2}yz^{3}$$

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

$$-6x^{6}y^{2}yz^{3}$$

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

Calculate -3 to the power of 2 and get 9.

$$9x^{4}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}$$

Multiply 9 and -\frac{2}{3} to get -6.

$$-6x^{4}y^{2}x^{2}yz^{3}$$

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

$$-6x^{6}y^{2}yz^{3}$$

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

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