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

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

Evaluate

$$-162z^{6}y^{15}x^{16}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 4 and get 81.

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

Multiply -2 and 81 to get -162.

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

To multiply powers of the same base, add their exponents. Add 4 and 12 to get 16.

$$-162x^{16}y^{3}z^{2}y^{12}z^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-162x^{16}y^{15}z^{2}z^{4}$$

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

$$-162x^{16}y^{15}z^{6}$$

Expand

$$-162z^{6}y^{15}x^{16}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 4 and get 81.

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

Multiply -2 and 81 to get -162.

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

To multiply powers of the same base, add their exponents. Add 4 and 12 to get 16.

$$-162x^{16}y^{3}z^{2}y^{12}z^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-162x^{16}y^{15}z^{2}z^{4}$$

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

$$-162x^{16}y^{15}z^{6}$$