Solve -4ab(-1/2ab^2)^2=

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

Evaluate

$$-a^{3}b^{5}$$

Solution Steps

Expand \left(-\frac{1}{2}ab^{2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

Multiply -4 and \frac{1}{4} to get -1.

$$-aba^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-a^{3}bb^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$-a^{3}b^{5}$$

Expand

$$-a^{3}b^{5}$$

Solution Steps

Expand \left(-\frac{1}{2}ab^{2}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

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

Multiply -4 and \frac{1}{4} to get -1.

$$-aba^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-a^{3}bb^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$-a^{3}b^{5}$$