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

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

Evaluate

$$8y^{11}\left(xz\right)^{5}$$

Solution Steps

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

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

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

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

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

$$\left(-x^{2}\right)y^{2}z^{2}\left(-8\right)x^{3}y^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$\left(-x^{2}\right)y^{11}z^{2}\left(-8\right)x^{3}z^{3}$$

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

$$\left(-x^{2}\right)y^{11}z^{5}\left(-8\right)x^{3}$$

Multiply -1 and -8 to get 8.

$$8x^{2}y^{11}z^{5}x^{3}$$

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

$$8x^{5}y^{11}z^{5}$$

Expand

$$8y^{11}\left(xz\right)^{5}$$

Solution Steps

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

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

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

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

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

$$\left(-x^{2}\right)y^{2}z^{2}\left(-8\right)x^{3}y^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 9 to get 11.

$$\left(-x^{2}\right)y^{11}z^{2}\left(-8\right)x^{3}z^{3}$$

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

$$\left(-x^{2}\right)y^{11}z^{5}\left(-8\right)x^{3}$$

Multiply -1 and -8 to get 8.

$$8x^{2}y^{11}z^{5}x^{3}$$

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

$$8x^{5}y^{11}z^{5}$$