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

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

Evaluate

$$z^{8}\left(xy\right)^{6}$$

Solution Steps

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

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

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

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

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

$$\left(-x\right)^{2}y^{6}z^{8}\left(-x^{2}\right)^{2}$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}y^{6}z^{8}\left(-x^{2}\right)^{2}$$

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

$$x^{2}y^{6}z^{8}\left(x^{2}\right)^{2}$$

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

$$x^{2}y^{6}z^{8}x^{4}$$

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

$$x^{6}y^{6}z^{8}$$

Expand

$$z^{8}\left(xy\right)^{6}$$

Solution Steps

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

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

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

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

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

$$\left(-x\right)^{2}y^{6}z^{8}\left(-x^{2}\right)^{2}$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}y^{6}z^{8}\left(-x^{2}\right)^{2}$$

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

$$x^{2}y^{6}z^{8}\left(x^{2}\right)^{2}$$

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

$$x^{2}y^{6}z^{8}x^{4}$$

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

$$x^{6}y^{6}z^{8}$$