Solve 8a^{4}b^{3}c^{2}(2a^2b^3)*(-1/2a^2bc^2)

$$8 a ^ { 4 } b ^ { 3 } c ^ { 2 } ( 2 a ^ { 2 } b ^ { 3 } ) \cdot ( - \frac { 1 } { 2 } a ^ { 2 } b c ^ { 2 } )$$

Evaluate

$$-8c^{4}b^{7}a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

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

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

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

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

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

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

$$8a^{8}b^{7}c^{2}\times 2\left(-\frac{1}{2}\right)c^{2}$$

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

$$8a^{8}b^{7}c^{4}\times 2\left(-\frac{1}{2}\right)$$

Multiply 8 and 2 to get 16.

$$16a^{8}b^{7}c^{4}\left(-\frac{1}{2}\right)$$

Multiply 16 and -\frac{1}{2} to get -8.

$$-8a^{8}b^{7}c^{4}$$

Differentiate w.r.t. c

$$-32c^{3}b^{7}a^{8}$$