Solve (-3x^2y)^2*2/3xyz*3/4xz^2

$$( - 3 x ^ { 2 } y ) ^ { 2 } \cdot \frac { 2 } { 3 } x y z \cdot \frac { 3 } { 4 } x z ^ { 2 }$$

Evaluate

$$\frac{9x^{6}\left(yz\right)^{3}}{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$9x^{4}y^{2}\times \frac{2}{3}x^{2}yz^{3}\times \frac{3}{4}$$

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

$$6x^{4}y^{2}x^{2}yz^{3}\times \frac{3}{4}$$

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

$$6x^{6}y^{2}yz^{3}\times \frac{3}{4}$$

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

$$6x^{6}y^{3}z^{3}\times \frac{3}{4}$$

Multiply 6 and \frac{3}{4} to get \frac{9}{2}.

$$\frac{9}{2}x^{6}y^{3}z^{3}$$

Expand

$$\frac{9x^{6}\left(yz\right)^{3}}{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$9x^{4}y^{2}\times \frac{2}{3}x^{2}yz^{3}\times \frac{3}{4}$$

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

$$6x^{4}y^{2}x^{2}yz^{3}\times \frac{3}{4}$$

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

$$6x^{6}y^{2}yz^{3}\times \frac{3}{4}$$

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

$$6x^{6}y^{3}z^{3}\times \frac{3}{4}$$

Multiply 6 and \frac{3}{4} to get \frac{9}{2}.

$$\frac{9}{2}x^{6}y^{3}z^{3}$$