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

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

Evaluate

$$27x^{10}\left(yz\right)^{11}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate -3 to the power of 3 and get -27.

$$\left(-x\right)y^{2}z^{2}\left(-27\right)x^{9}y^{9}z^{9}$$

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

$$\left(-x\right)y^{11}z^{2}\left(-27\right)x^{9}z^{9}$$

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

$$\left(-x\right)y^{11}z^{11}\left(-27\right)x^{9}$$

Multiply -1 and -27 to get 27.

$$27xy^{11}z^{11}x^{9}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$27x^{10}y^{11}z^{11}$$

Expand

$$27x^{10}\left(yz\right)^{11}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate -3 to the power of 3 and get -27.

$$\left(-x\right)y^{2}z^{2}\left(-27\right)x^{9}y^{9}z^{9}$$

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

$$\left(-x\right)y^{11}z^{2}\left(-27\right)x^{9}z^{9}$$

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

$$\left(-x\right)y^{11}z^{11}\left(-27\right)x^{9}$$

Multiply -1 and -27 to get 27.

$$27xy^{11}z^{11}x^{9}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$27x^{10}y^{11}z^{11}$$