Solve (4a^2b^-1)^-2

$$( 4 a ^ { 2 } b ^ { - 1 } ) ^ { - 2 }$$

Evaluate

$$\frac{b^{2}}{16a^{4}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power -2.

$$\frac{1}{16}\left(a^{2}\right)^{-2}\times \left(\frac{1}{b}\right)^{-2}$$

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

$$\frac{1}{16}a^{2\left(-2\right)}b^{-\left(-2\right)}$$

Multiply 2 times -2.

$$\frac{1}{16}\times \frac{1}{a^{4}}b^{-\left(-2\right)}$$

Multiply -1 times -2.

$$\frac{1}{16}\times \frac{1}{a^{4}}b^{2}$$

Expand

$$\frac{b^{2}}{16a^{4}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power -2.

$$\frac{1}{16}\left(a^{2}\right)^{-2}\times \left(\frac{1}{b}\right)^{-2}$$

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

$$\frac{1}{16}a^{2\left(-2\right)}b^{-\left(-2\right)}$$

Multiply 2 times -2.

$$\frac{1}{16}\times \frac{1}{a^{4}}b^{-\left(-2\right)}$$

Multiply -1 times -2.

$$\frac{1}{16}\times \frac{1}{a^{4}}b^{2}$$