Solve (-1/2ab^2)^2

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

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -\frac{1}{2} to the power 2.

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

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

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

Multiply 2 times 2.

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

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -\frac{1}{2} to the power 2.

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

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

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

Multiply 2 times 2.

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