Solve (-3x^{3}y^2z)^2(2y^2z^2)

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

Evaluate

$$18z^{4}\left(xy\right)^{6}$$

Solution Steps

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

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

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

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

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

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

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

$$9x^{6}y^{4}z^{2}\times 2y^{2}z^{2}$$

Multiply 9 and 2 to get 18.

$$18x^{6}y^{4}z^{2}y^{2}z^{2}$$

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

$$18x^{6}y^{6}z^{2}z^{2}$$

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

$$18x^{6}y^{6}z^{4}$$

Expand

$$18z^{4}\left(xy\right)^{6}$$

Solution Steps

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

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

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

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

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

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

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

$$9x^{6}y^{4}z^{2}\times 2y^{2}z^{2}$$

Multiply 9 and 2 to get 18.

$$18x^{6}y^{4}z^{2}y^{2}z^{2}$$

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

$$18x^{6}y^{6}z^{2}z^{2}$$

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

$$18x^{6}y^{6}z^{4}$$