Solve 8a^{4}b^{3}cdiv2a^2b^3*a^3bc^2

$$8 a ^ { 4 } b ^ { 3 } c \div 2 a ^ { 2 } b ^ { 3 } \cdot a ^ { 3 } b c ^ { 2 }$$

Evaluate

$$4c^{3}b^{7}a^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{8a^{4}b^{3}c}{2}a^{5}b^{3}bc^{2}$$

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

$$\frac{8a^{4}b^{3}c}{2}a^{5}b^{4}c^{2}$$

Divide 8a^{4}b^{3}c by 2 to get 4a^{4}b^{3}c.

$$4a^{4}b^{3}ca^{5}b^{4}c^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$4a^{9}b^{3}cb^{4}c^{2}$$

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

$$4a^{9}b^{7}cc^{2}$$

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

$$4a^{9}b^{7}c^{3}$$

Differentiate w.r.t. c

$$12c^{2}b^{7}a^{9}$$