Solve frac{2a^{3}b}{c^3b^2}div6ab^2/c^2=

$$\frac { 2 a ^ { 3 } b } { c ^ { 3 } b ^ { 2 } } \div \frac { 6 a b ^ { 2 } } { c ^ { 2 } } =$$

Evaluate

$$\frac{a^{2}}{3cb^{3}}$$

Solution Steps

Divide \frac{2a^{3}b}{c^{3}b^{2}} by \frac{6ab^{2}}{c^{2}} by multiplying \frac{2a^{3}b}{c^{3}b^{2}} by the reciprocal of \frac{6ab^{2}}{c^{2}}.

$$\frac{2a^{3}bc^{2}}{c^{3}b^{2}\times 6ab^{2}}$$

Cancel out 2abc^{2} in both numerator and denominator.

$$\frac{a^{2}}{3bcb^{2}}$$

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

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

Differentiate w.r.t. a

$$\frac{2a}{3cb^{3}}$$