Solve (3x^2z^3)^4=

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

Evaluate

$$81x^{8}z^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 4.

$$81\left(x^{2}\right)^{4}\left(z^{3}\right)^{4}$$

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

$$81x^{2\times 4}z^{3\times 4}$$

Multiply 2 times 4.

$$81x^{8}z^{3\times 4}$$

Multiply 3 times 4.

$$81x^{8}z^{12}$$

Expand

$$81x^{8}z^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 4.

$$81\left(x^{2}\right)^{4}\left(z^{3}\right)^{4}$$

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

$$81x^{2\times 4}z^{3\times 4}$$

Multiply 2 times 4.

$$81x^{8}z^{3\times 4}$$

Multiply 3 times 4.

$$81x^{8}z^{12}$$