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

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

Evaluate

$$16z^{8}x^{14}y^{16}$$

Solution Steps

Expand \left(-2x^{3}y^{3}z^{2}\right)^{4}.

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\left(-2\right)^{4}x^{12}y^{12}z^{8}x^{2}y^{4}$$

Calculate -2 to the power of 4 and get 16.

$$16x^{12}y^{12}z^{8}x^{2}y^{4}$$

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

$$16x^{14}y^{12}z^{8}y^{4}$$

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

$$16x^{14}y^{16}z^{8}$$

Expand

$$16z^{8}x^{14}y^{16}$$

Solution Steps

Expand \left(-2x^{3}y^{3}z^{2}\right)^{4}.

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

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\left(-2\right)^{4}x^{12}y^{12}z^{8}x^{2}y^{4}$$

Calculate -2 to the power of 4 and get 16.

$$16x^{12}y^{12}z^{8}x^{2}y^{4}$$

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

$$16x^{14}y^{12}z^{8}y^{4}$$

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

$$16x^{14}y^{16}z^{8}$$