Solve (2x^2y^5)^4

$$( 2 x ^ { 2 } y ^ { 5 } ) ^ { 4 }$$

Evaluate

$$16x^{8}y^{20}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2x^{2}y^{5}\right)^{4}$$

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

$$2^{4}\left(x^{2}\right)^{4}\left(y^{5}\right)^{4}$$

Raise 2 to the power 4.

$$16\left(x^{2}\right)^{4}\left(y^{5}\right)^{4}$$

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

$$16x^{2\times 4}y^{5\times 4}$$

Multiply 2 times 4.

$$16x^{8}y^{5\times 4}$$

Multiply 5 times 4.

$$16x^{8}y^{20}$$

Expand

$$16x^{8}y^{20}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2x^{2}y^{5}\right)^{4}$$

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

$$2^{4}\left(x^{2}\right)^{4}\left(y^{5}\right)^{4}$$

Raise 2 to the power 4.

$$16\left(x^{2}\right)^{4}\left(y^{5}\right)^{4}$$

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

$$16x^{2\times 4}y^{5\times 4}$$

Multiply 2 times 4.

$$16x^{8}y^{5\times 4}$$

Multiply 5 times 4.

$$16x^{8}y^{20}$$