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

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

Evaluate

$$-2z^{5}y^{8}x^{10}$$

Solution Steps

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

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

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

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

Calculate -x^{4} to the power of 2 and get \left(x^{4}\right)^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-2x^{2}y^{8}z^{3}\left(x^{4}\right)^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-2x^{2}y^{8}z^{5}\left(x^{4}\right)^{2}$$

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

$$-2x^{2}y^{8}z^{5}x^{8}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$-2x^{10}y^{8}z^{5}$$

Expand

$$-2z^{5}y^{8}x^{10}$$

Solution Steps

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

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

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

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

Calculate -x^{4} to the power of 2 and get \left(x^{4}\right)^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-2x^{2}y^{8}z^{3}\left(x^{4}\right)^{2}z^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-2x^{2}y^{8}z^{5}\left(x^{4}\right)^{2}$$

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

$$-2x^{2}y^{8}z^{5}x^{8}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$-2x^{10}y^{8}z^{5}$$