Solve (2x^4y^4)^4

$$( 2 x ^ { 4 } y ^ { 4 } ) ^ { 4 }$$

Evaluate

$$16\left(xy\right)^{16}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power 4.

$$16\left(x^{4}\right)^{4}\left(y^{4}\right)^{4}$$

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

$$16x^{4\times 4}y^{4\times 4}$$

Multiply 4 times 4.

$$16x^{16}y^{4\times 4}$$

Multiply 4 times 4.

$$16x^{16}y^{16}$$

Expand

$$16\left(xy\right)^{16}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power 4.

$$16\left(x^{4}\right)^{4}\left(y^{4}\right)^{4}$$

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

$$16x^{4\times 4}y^{4\times 4}$$

Multiply 4 times 4.

$$16x^{16}y^{4\times 4}$$

Multiply 4 times 4.

$$16x^{16}y^{16}$$