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

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

Evaluate

$$-8\left(xz\right)^{4}y^{13}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-2\right)^{3}y^{9}\left(\left(-x^{2}\right)y^{2}z^{2}\right)^{2}$$

Calculate -2 to the power of 3 and get -8.

$$-8y^{9}\left(\left(-x^{2}\right)y^{2}z^{2}\right)^{2}$$

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

$$-8y^{9}\left(-x^{2}\right)^{2}\left(y^{2}\right)^{2}\left(z^{2}\right)^{2}$$

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

$$-8y^{9}\left(-x^{2}\right)^{2}y^{4}\left(z^{2}\right)^{2}$$

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

$$-8y^{9}\left(-x^{2}\right)^{2}y^{4}z^{4}$$

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

$$-8y^{9}\left(x^{2}\right)^{2}y^{4}z^{4}$$

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$-8y^{13}\left(x^{2}\right)^{2}z^{4}$$

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

$$-8y^{13}x^{4}z^{4}$$

Expand

$$-8\left(xz\right)^{4}y^{13}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-2\right)^{3}y^{9}\left(\left(-x^{2}\right)y^{2}z^{2}\right)^{2}$$

Calculate -2 to the power of 3 and get -8.

$$-8y^{9}\left(\left(-x^{2}\right)y^{2}z^{2}\right)^{2}$$

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

$$-8y^{9}\left(-x^{2}\right)^{2}\left(y^{2}\right)^{2}\left(z^{2}\right)^{2}$$

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

$$-8y^{9}\left(-x^{2}\right)^{2}y^{4}\left(z^{2}\right)^{2}$$

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

$$-8y^{9}\left(-x^{2}\right)^{2}y^{4}z^{4}$$

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

$$-8y^{9}\left(x^{2}\right)^{2}y^{4}z^{4}$$

To multiply powers of the same base, add their exponents. Add 9 and 4 to get 13.

$$-8y^{13}\left(x^{2}\right)^{2}z^{4}$$

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

$$-8y^{13}x^{4}z^{4}$$