Solve (-2a^3b^3)(1/2ab^2)^2

$$( - 2 a ^ { 3 } b ^ { 3 } ) ( \frac { 1 } { 2 } a b ^ { 2 } ) ^ { 2 }$$

Evaluate

$$-\frac{a^{5}b^{7}}{2}$$

Solution Steps

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

$$-2a^{3}b^{3}\times \left(\frac{1}{2}\right)^{2}a^{2}\left(b^{2}\right)^{2}$$

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

$$-2a^{3}b^{3}\times \left(\frac{1}{2}\right)^{2}a^{2}b^{4}$$

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

$$-2a^{3}b^{3}\times \frac{1}{4}a^{2}b^{4}$$

Multiply -2 and \frac{1}{4} to get -\frac{1}{2}.

$$-\frac{1}{2}a^{3}b^{3}a^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-\frac{1}{2}a^{5}b^{3}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-\frac{1}{2}a^{5}b^{7}$$

Expand

$$-\frac{a^{5}b^{7}}{2}$$

Solution Steps

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

$$-2a^{3}b^{3}\times \left(\frac{1}{2}\right)^{2}a^{2}\left(b^{2}\right)^{2}$$

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

$$-2a^{3}b^{3}\times \left(\frac{1}{2}\right)^{2}a^{2}b^{4}$$

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

$$-2a^{3}b^{3}\times \frac{1}{4}a^{2}b^{4}$$

Multiply -2 and \frac{1}{4} to get -\frac{1}{2}.

$$-\frac{1}{2}a^{3}b^{3}a^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-\frac{1}{2}a^{5}b^{3}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-\frac{1}{2}a^{5}b^{7}$$