Solve (-3x^3z)^4(2x^2y^2)3

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

Evaluate

$$486y^{2}z^{4}x^{14}$$

Solution Steps

Expand \left(-3x^{3}z\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(-3\right)^{4}x^{12}z^{4}\times 2x^{2}y^{2}\times 3$$

Calculate -3 to the power of 4 and get 81.

$$81x^{12}z^{4}\times 2x^{2}y^{2}\times 3$$

Multiply 81 and 2 to get 162.

$$162x^{12}z^{4}x^{2}y^{2}\times 3$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$162x^{14}z^{4}y^{2}\times 3$$

Multiply 162 and 3 to get 486.

$$486x^{14}z^{4}y^{2}$$

Expand

$$486y^{2}z^{4}x^{14}$$

Solution Steps

Expand \left(-3x^{3}z\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\left(-3\right)^{4}x^{12}z^{4}\times 2x^{2}y^{2}\times 3$$

Calculate -3 to the power of 4 and get 81.

$$81x^{12}z^{4}\times 2x^{2}y^{2}\times 3$$

Multiply 81 and 2 to get 162.

$$162x^{12}z^{4}x^{2}y^{2}\times 3$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$162x^{14}z^{4}y^{2}\times 3$$

Multiply 162 and 3 to get 486.

$$486x^{14}z^{4}y^{2}$$