Solve (-c^8)(-4a^6bc)(8a^6b)

$$( - c ^ { 8 } ) ( - 4 a ^ { 6 } b c ) ( 8 a ^ { 6 } b )$$

Evaluate

$$32b^{2}c^{9}a^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\left(-c^{8}\right)\left(-4\right)a^{12}bc\times 8b$$

Multiply b and b to get b^{2}.

$$\left(-c^{8}\right)\left(-4\right)a^{12}b^{2}c\times 8$$

Multiply -4 and 8 to get -32.

$$\left(-c^{8}\right)\left(-32\right)a^{12}b^{2}c$$

Multiply -1 and -32 to get 32.

$$32c^{8}a^{12}b^{2}c$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$32c^{9}a^{12}b^{2}$$

Differentiate w.r.t. c

$$288b^{2}c^{8}a^{12}$$