Solve [(-xy^2z^3)^2]^3

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

Evaluate

$$x^{6}y^{12}z^{18}$$

Solution Steps

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

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

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

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

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

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

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

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

Expand \left(x^{2}y^{4}z^{6}\right)^{3}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$x^{6}y^{12}\left(z^{6}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$x^{6}y^{12}z^{18}$$

Expand

$$x^{6}y^{12}z^{18}$$

Solution Steps

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

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

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

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

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

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

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

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

Expand \left(x^{2}y^{4}z^{6}\right)^{3}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$x^{6}y^{12}\left(z^{6}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$x^{6}y^{12}z^{18}$$