Solve -6a^2b{left(1/2abcright)}^2

$$-6 { a }^{ 2 } b { \left( \frac{ 1 }{ 2 } abc \right) }^{ 2 }$$

Evaluate

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

Solution Steps

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

$$-6a^{2}b\times \left(\frac{1}{2}\right)^{2}a^{2}b^{2}c^{2}$$

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

$$-6a^{2}b\times \frac{1}{4}a^{2}b^{2}c^{2}$$

Multiply -6 and \frac{1}{4} to get -\frac{3}{2}.

$$-\frac{3}{2}a^{2}ba^{2}b^{2}c^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-\frac{3}{2}a^{4}bb^{2}c^{2}$$

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

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

Expand

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

Solution Steps

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

$$-6a^{2}b\times \left(\frac{1}{2}\right)^{2}a^{2}b^{2}c^{2}$$

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

$$-6a^{2}b\times \frac{1}{4}a^{2}b^{2}c^{2}$$

Multiply -6 and \frac{1}{4} to get -\frac{3}{2}.

$$-\frac{3}{2}a^{2}ba^{2}b^{2}c^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-\frac{3}{2}a^{4}bb^{2}c^{2}$$

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

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