Solve (9g^8h^8)^2

$$( 9 g ^ { 8 } h ^ { 8 } ) ^ { 2 }$$

Evaluate

$$81\left(gh\right)^{16}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(9g^{8}h^{8}\right)^{2}$$

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

$$9^{2}\left(g^{8}\right)^{2}\left(h^{8}\right)^{2}$$

Raise 9 to the power 2.

$$81\left(g^{8}\right)^{2}\left(h^{8}\right)^{2}$$

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

$$81g^{8\times 2}h^{8\times 2}$$

Multiply 8 times 2.

$$81g^{16}h^{8\times 2}$$

Multiply 8 times 2.

$$81g^{16}h^{16}$$

Expand

$$81\left(gh\right)^{16}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(9g^{8}h^{8}\right)^{2}$$

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

$$9^{2}\left(g^{8}\right)^{2}\left(h^{8}\right)^{2}$$

Raise 9 to the power 2.

$$81\left(g^{8}\right)^{2}\left(h^{8}\right)^{2}$$

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

$$81g^{8\times 2}h^{8\times 2}$$

Multiply 8 times 2.

$$81g^{16}h^{8\times 2}$$

Multiply 8 times 2.

$$81g^{16}h^{16}$$