Solve (-4a^{3}bc^{2})(a^3b^2c)(3ab^4c^5

$$( - 4 a ^ { 3 } b c ^ { 2 } ) ( a ^ { 3 } b ^ { 2 } c ) ( 3 a b ^ { 4 } c ^ { 5 }$$

Evaluate

$$-12c^{8}\left(ab\right)^{7}$$

Solution Steps

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

$$-4a^{6}bc^{2}b^{2}c\times 3ab^{4}c^{5}$$

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

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

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$-4a^{7}b^{7}c^{8}\times 3$$

Multiply -4 and 3 to get -12.

$$-12a^{7}b^{7}c^{8}$$

Differentiate w.r.t. a

$$-84a^{6}b^{7}c^{8}$$