Solve (-4y^4z^-2)^-2

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

Evaluate

$$\frac{z^{4}}{16y^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -4 to the power -2.

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

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

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

Multiply 4 times -2.

$$\frac{1}{16}\times \frac{1}{y^{8}}z^{-2\left(-2\right)}$$

Multiply -2 times -2.

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

Expand

$$\frac{z^{4}}{16y^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -4 to the power -2.

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

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

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

Multiply 4 times -2.

$$\frac{1}{16}\times \frac{1}{y^{8}}z^{-2\left(-2\right)}$$

Multiply -2 times -2.

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