Solve (9v^2K^2)^2

$$( 9 v ^ { 2 } K ^ { 2 } ) ^ { 2 }$$

Evaluate

$$81\left(Kv\right)^{4}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(9v^{2}K^{2}\right)^{2}$$

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

$$9^{2}\left(v^{2}\right)^{2}\left(K^{2}\right)^{2}$$

Raise 9 to the power 2.

$$81\left(v^{2}\right)^{2}\left(K^{2}\right)^{2}$$

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

$$81v^{2\times 2}K^{2\times 2}$$

Multiply 2 times 2.

$$81v^{4}K^{2\times 2}$$

Multiply 2 times 2.

$$81v^{4}K^{4}$$

Expand

$$81\left(Kv\right)^{4}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(9v^{2}K^{2}\right)^{2}$$

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

$$9^{2}\left(v^{2}\right)^{2}\left(K^{2}\right)^{2}$$

Raise 9 to the power 2.

$$81\left(v^{2}\right)^{2}\left(K^{2}\right)^{2}$$

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

$$81v^{2\times 2}K^{2\times 2}$$

Multiply 2 times 2.

$$81v^{4}K^{2\times 2}$$

Multiply 2 times 2.

$$81v^{4}K^{4}$$