Solve left(4x^4y^3z^3right)^4

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

Evaluate

$$256x^{16}\left(yz\right)^{12}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 4.

$$256\left(x^{4}\right)^{4}\left(y^{3}\right)^{4}\left(z^{3}\right)^{4}$$

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

$$256x^{4\times 4}y^{3\times 4}z^{3\times 4}$$

Multiply 4 times 4.

$$256x^{16}y^{3\times 4}z^{3\times 4}$$

Multiply 3 times 4.

$$256x^{16}y^{12}z^{3\times 4}$$

Multiply 3 times 4.

$$256x^{16}y^{12}z^{12}$$

Expand

$$256x^{16}\left(yz\right)^{12}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power 4.

$$256\left(x^{4}\right)^{4}\left(y^{3}\right)^{4}\left(z^{3}\right)^{4}$$

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

$$256x^{4\times 4}y^{3\times 4}z^{3\times 4}$$

Multiply 4 times 4.

$$256x^{16}y^{3\times 4}z^{3\times 4}$$

Multiply 3 times 4.

$$256x^{16}y^{12}z^{3\times 4}$$

Multiply 3 times 4.

$$256x^{16}y^{12}z^{12}$$