Solve (-2xy^2)^-4

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

Evaluate

$$\frac{1}{16x^{4}y^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-2x^{1}y^{2}\right)^{-4}$$

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

$$\left(-2\right)^{-4}\left(x^{1}\right)^{-4}\left(y^{2}\right)^{-4}$$

Raise -2 to the power -4.

$$\frac{1}{16}\left(x^{1}\right)^{-4}\left(y^{2}\right)^{-4}$$

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

$$\frac{1}{16}x^{-4}y^{2\left(-4\right)}$$

Multiply 2 times -4.

$$\frac{1}{16}\times \frac{1}{x^{4}}\times \frac{1}{y^{8}}$$

Expand

$$\frac{1}{16x^{4}y^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-2x^{1}y^{2}\right)^{-4}$$

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

$$\left(-2\right)^{-4}\left(x^{1}\right)^{-4}\left(y^{2}\right)^{-4}$$

Raise -2 to the power -4.

$$\frac{1}{16}\left(x^{1}\right)^{-4}\left(y^{2}\right)^{-4}$$

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

$$\frac{1}{16}x^{-4}y^{2\left(-4\right)}$$

Multiply 2 times -4.

$$\frac{1}{16}\times \frac{1}{x^{4}}\times \frac{1}{y^{8}}$$