Solve (-1/2ab^{2})^3*(6a^2bc^3)*(-2ac)^2

$$( - \frac { 1 } { 2 } a b ^ { 2 } ) ^ { 3 } \times ( 6 a ^ { 2 } b c ^ { 3 } ) \times ( - 2 a c ) ^ { 2 }$$

Evaluate

$$-3c^{5}\left(ab\right)^{7}$$

Solution Steps

Expand \left(-\frac{1}{2}ab^{2}\right)^{3}.

$$\left(-\frac{1}{2}\right)^{3}a^{3}\left(b^{2}\right)^{3}\times 6a^{2}bc^{3}\left(-2ac\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(-\frac{1}{2}\right)^{3}a^{3}b^{6}\times 6a^{2}bc^{3}\left(-2ac\right)^{2}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$-\frac{1}{8}a^{3}b^{6}\times 6a^{2}bc^{3}\left(-2ac\right)^{2}$$

Multiply -\frac{1}{8} and 6 to get -\frac{3}{4}.

$$-\frac{3}{4}a^{3}b^{6}a^{2}bc^{3}\left(-2ac\right)^{2}$$

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

$$-\frac{3}{4}a^{5}b^{6}bc^{3}\left(-2ac\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-\frac{3}{4}a^{5}b^{7}c^{3}\left(-2ac\right)^{2}$$

Expand \left(-2ac\right)^{2}.

$$-\frac{3}{4}a^{5}b^{7}c^{3}\left(-2\right)^{2}a^{2}c^{2}$$

Calculate -2 to the power of 2 and get 4.

$$-\frac{3}{4}a^{5}b^{7}c^{3}\times 4a^{2}c^{2}$$

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

$$-3a^{5}b^{7}c^{3}a^{2}c^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-3a^{7}b^{7}c^{3}c^{2}$$

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

$$-3a^{7}b^{7}c^{5}$$

Expand

$$-3c^{5}\left(ab\right)^{7}$$

Solution Steps

Expand \left(-\frac{1}{2}ab^{2}\right)^{3}.

$$\left(-\frac{1}{2}\right)^{3}a^{3}\left(b^{2}\right)^{3}\times 6a^{2}bc^{3}\left(-2ac\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(-\frac{1}{2}\right)^{3}a^{3}b^{6}\times 6a^{2}bc^{3}\left(-2ac\right)^{2}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$-\frac{1}{8}a^{3}b^{6}\times 6a^{2}bc^{3}\left(-2ac\right)^{2}$$

Multiply -\frac{1}{8} and 6 to get -\frac{3}{4}.

$$-\frac{3}{4}a^{3}b^{6}a^{2}bc^{3}\left(-2ac\right)^{2}$$

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

$$-\frac{3}{4}a^{5}b^{6}bc^{3}\left(-2ac\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$-\frac{3}{4}a^{5}b^{7}c^{3}\left(-2ac\right)^{2}$$

Expand \left(-2ac\right)^{2}.

$$-\frac{3}{4}a^{5}b^{7}c^{3}\left(-2\right)^{2}a^{2}c^{2}$$

Calculate -2 to the power of 2 and get 4.

$$-\frac{3}{4}a^{5}b^{7}c^{3}\times 4a^{2}c^{2}$$

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

$$-3a^{5}b^{7}c^{3}a^{2}c^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-3a^{7}b^{7}c^{3}c^{2}$$

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

$$-3a^{7}b^{7}c^{5}$$