Solve (2a^-2b^2)^-2

$$( 2 a ^ { - 2 } b ^ { 2 } ) ^ { - 2 }$$

Evaluate

$$\frac{\left(\frac{a}{b}\right)^{4}}{4}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2a^{-2}b^{2}\right)^{-2}$$

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

$$2^{-2}\left(a^{-2}\right)^{-2}\left(b^{2}\right)^{-2}$$

Raise 2 to the power -2.

$$\frac{1}{4}\left(a^{-2}\right)^{-2}\left(b^{2}\right)^{-2}$$

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

$$\frac{1}{4}a^{-2\left(-2\right)}b^{2\left(-2\right)}$$

Multiply -2 times -2.

$$\frac{1}{4}a^{4}b^{2\left(-2\right)}$$

Multiply 2 times -2.

$$\frac{1}{4}a^{4}\times \frac{1}{b^{4}}$$

Expand

$$\frac{\left(\frac{a}{b}\right)^{4}}{4}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2a^{-2}b^{2}\right)^{-2}$$

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

$$2^{-2}\left(a^{-2}\right)^{-2}\left(b^{2}\right)^{-2}$$

Raise 2 to the power -2.

$$\frac{1}{4}\left(a^{-2}\right)^{-2}\left(b^{2}\right)^{-2}$$

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

$$\frac{1}{4}a^{-2\left(-2\right)}b^{2\left(-2\right)}$$

Multiply -2 times -2.

$$\frac{1}{4}a^{4}b^{2\left(-2\right)}$$

Multiply 2 times -2.

$$\frac{1}{4}a^{4}\times \frac{1}{b^{4}}$$