Solve (2y^-2z^6)^-2

$$( 2 y ^ { - 2 } z ^ { 6 } ) ^ { - 2 }$$

Evaluate

$$\frac{y^{4}}{4z^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2y^{-2}z^{6}\right)^{-2}$$

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

$$2^{-2}\left(y^{-2}\right)^{-2}\left(z^{6}\right)^{-2}$$

Raise 2 to the power -2.

$$\frac{1}{4}\left(y^{-2}\right)^{-2}\left(z^{6}\right)^{-2}$$

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

$$\frac{1}{4}y^{-2\left(-2\right)}z^{6\left(-2\right)}$$

Multiply -2 times -2.

$$\frac{1}{4}y^{4}z^{6\left(-2\right)}$$

Multiply 6 times -2.

$$\frac{1}{4}y^{4}\times \frac{1}{z^{12}}$$

Expand

$$\frac{y^{4}}{4z^{12}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2y^{-2}z^{6}\right)^{-2}$$

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

$$2^{-2}\left(y^{-2}\right)^{-2}\left(z^{6}\right)^{-2}$$

Raise 2 to the power -2.

$$\frac{1}{4}\left(y^{-2}\right)^{-2}\left(z^{6}\right)^{-2}$$

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

$$\frac{1}{4}y^{-2\left(-2\right)}z^{6\left(-2\right)}$$

Multiply -2 times -2.

$$\frac{1}{4}y^{4}z^{6\left(-2\right)}$$

Multiply 6 times -2.

$$\frac{1}{4}y^{4}\times \frac{1}{z^{12}}$$