Solve -ab^3*2abc^2*(a^2)^3

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

Evaluate

$$-2c^{2}b^{4}a^{8}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(-a\right)b^{3}\times 2abc^{2}a^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(-a\right)b^{4}\times 2ac^{2}a^{6}$$

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

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

Multiply -1 and 2 to get -2.

$$-2ab^{4}a^{7}c^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$-2a^{8}b^{4}c^{2}$$

Differentiate w.r.t. c

$$-4cb^{4}a^{8}$$