Solve frac{frac{3a^{4}b^{3}}{7b^4c}}{15a^2b^6/14ac^7}

$$\frac { \frac { 3 a ^ { 4 } b ^ { 3 } } { 7 b ^ { 4 } c } } { \frac { 15 a ^ { 2 } b ^ { 6 } } { 14 a c ^ { 7 } } }$$

Evaluate

$$\frac{2a^{3}c^{6}}{5b^{7}}$$

Solution Steps

Divide \frac{3a^{4}b^{3}}{7b^{4}c} by \frac{15a^{2}b^{6}}{14ac^{7}} by multiplying \frac{3a^{4}b^{3}}{7b^{4}c} by the reciprocal of \frac{15a^{2}b^{6}}{14ac^{7}}.

$$\frac{3a^{4}b^{3}\times 14ac^{7}}{7b^{4}c\times 15a^{2}b^{6}}$$

Cancel out 3\times 7ca^{2}b^{3} in both numerator and denominator.

$$\frac{2aa^{2}c^{6}}{5bb^{6}}$$

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

$$\frac{2a^{3}c^{6}}{5bb^{6}}$$

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

$$\frac{2a^{3}c^{6}}{5b^{7}}$$

Differentiate w.r.t. c

$$\frac{12a^{3}c^{5}}{5b^{7}}$$