Solve -3ea^3b^2c^412a^7b{c}^6

$$-3e { a }^{ 3 } { b }^{ 2 } { c }^{ 4 } 12 { a }^{ 7 } b { c }^{ 6 }$$

Evaluate

$$-36eb^{3}\left(ac\right)^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$-3ea^{10}b^{2}c^{4}\times 12bc^{6}$$

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

$$-3ea^{10}b^{3}c^{4}\times 12c^{6}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$-3ea^{10}b^{3}c^{10}\times 12$$

Multiply -3 and 12 to get -36.

$$-36ea^{10}b^{3}c^{10}$$

Differentiate w.r.t. a

$$-360eb^{3}a^{9}c^{10}$$