Solve (-3a^3b^2)*(-2ab^4c)^3

$$( - 3 a ^ { 3 } b ^ { 2 } ) \cdot ( - 2 a b ^ { 4 } c ) ^ { 3 }$$

Evaluate

$$24c^{3}a^{6}b^{14}$$

Solution Steps

Expand \left(-2ab^{4}c\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$-3a^{3}b^{2}\left(-2\right)^{3}a^{3}b^{12}c^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-3a^{3}b^{2}\left(-8\right)a^{3}b^{12}c^{3}$$

Multiply -3 and -8 to get 24.

$$24a^{3}b^{2}a^{3}b^{12}c^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$24a^{6}b^{2}b^{12}c^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$24a^{6}b^{14}c^{3}$$

Expand

$$24c^{3}a^{6}b^{14}$$

Solution Steps

Expand \left(-2ab^{4}c\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$-3a^{3}b^{2}\left(-2\right)^{3}a^{3}b^{12}c^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-3a^{3}b^{2}\left(-8\right)a^{3}b^{12}c^{3}$$

Multiply -3 and -8 to get 24.

$$24a^{3}b^{2}a^{3}b^{12}c^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$24a^{6}b^{2}b^{12}c^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 12 to get 14.

$$24a^{6}b^{14}c^{3}$$