Solve left(xy^2z^3right)^6

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

Evaluate

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

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(x^{1}y^{2}z^{3}\right)^{6}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$1^{6}\left(x^{1}\right)^{6}\left(y^{2}\right)^{6}\left(z^{3}\right)^{6}$$

To raise a power to another power, multiply the exponents.

$$x^{6}y^{2\times 6}z^{3\times 6}$$

Multiply 2 times 6.

$$x^{6}y^{12}z^{3\times 6}$$

Multiply 3 times 6.

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

Expand

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

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(x^{1}y^{2}z^{3}\right)^{6}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$1^{6}\left(x^{1}\right)^{6}\left(y^{2}\right)^{6}\left(z^{3}\right)^{6}$$

To raise a power to another power, multiply the exponents.

$$x^{6}y^{2\times 6}z^{3\times 6}$$

Multiply 2 times 6.

$$x^{6}y^{12}z^{3\times 6}$$

Multiply 3 times 6.

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