Solve (3p^2q^2)^4

$$( 3 p ^ { 2 } q ^ { 2 } ) ^ { 4 }$$

Evaluate

$$81\left(pq\right)^{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3p^{2}q^{2}\right)^{4}$$

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

$$3^{4}\left(p^{2}\right)^{4}\left(q^{2}\right)^{4}$$

Raise 3 to the power 4.

$$81\left(p^{2}\right)^{4}\left(q^{2}\right)^{4}$$

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

$$81p^{2\times 4}q^{2\times 4}$$

Multiply 2 times 4.

$$81p^{8}q^{2\times 4}$$

Multiply 2 times 4.

$$81p^{8}q^{8}$$

Expand

$$81\left(pq\right)^{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3p^{2}q^{2}\right)^{4}$$

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

$$3^{4}\left(p^{2}\right)^{4}\left(q^{2}\right)^{4}$$

Raise 3 to the power 4.

$$81\left(p^{2}\right)^{4}\left(q^{2}\right)^{4}$$

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

$$81p^{2\times 4}q^{2\times 4}$$

Multiply 2 times 4.

$$81p^{8}q^{2\times 4}$$

Multiply 2 times 4.

$$81p^{8}q^{8}$$