Solve (xy^2z^3)^4

$$( x y ^ { 2 } z ^ { 3 } ) ^ { 4 }$$

Evaluate

$$x^{4}y^{8}z^{12}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(x^{1}y^{2}z^{3}\right)^{4}$$

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

$$1^{4}\left(x^{1}\right)^{4}\left(y^{2}\right)^{4}\left(z^{3}\right)^{4}$$

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

$$x^{4}y^{2\times 4}z^{3\times 4}$$

Multiply 2 times 4.

$$x^{4}y^{8}z^{3\times 4}$$

Multiply 3 times 4.

$$x^{4}y^{8}z^{12}$$

Expand

$$x^{4}y^{8}z^{12}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(x^{1}y^{2}z^{3}\right)^{4}$$

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

$$1^{4}\left(x^{1}\right)^{4}\left(y^{2}\right)^{4}\left(z^{3}\right)^{4}$$

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

$$x^{4}y^{2\times 4}z^{3\times 4}$$

Multiply 2 times 4.

$$x^{4}y^{8}z^{3\times 4}$$

Multiply 3 times 4.

$$x^{4}y^{8}z^{12}$$