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

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

Evaluate

$$16\times \left(\frac{x}{y}\right)^{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 4.

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

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

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

Multiply 2 times 4.

$$16x^{8}y^{-2\times 4}$$

Multiply -2 times 4.

$$16x^{8}\times \frac{1}{y^{8}}$$

Expand

$$16\times \left(\frac{x}{y}\right)^{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 4.

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

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

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

Multiply 2 times 4.

$$16x^{8}y^{-2\times 4}$$

Multiply -2 times 4.

$$16x^{8}\times \frac{1}{y^{8}}$$