Solve 51a^2bc^3:9a^3b^2c

$$51 a ^ { 2 } b c ^ { 3 } : 9 a ^ { 3 } b ^ { 2 } c$$

Evaluate

$$\frac{17b^{3}c^{4}a^{5}}{3}$$

Solution Steps

Divide 51a^{2}bc^{3} by 9 to get \frac{17}{3}a^{2}bc^{3}.

$$\frac{17}{3}a^{2}bc^{3}a^{3}b^{2}c$$

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

$$\frac{17}{3}a^{5}bc^{3}b^{2}c$$

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

$$\frac{17}{3}a^{5}b^{3}c^{3}c$$

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

$$\frac{17}{3}a^{5}b^{3}c^{4}$$

Differentiate w.r.t. a

$$\frac{85b^{3}\left(ac\right)^{4}}{3}$$