Solve frac{a^{3}*b^{2}*a^4}{c^2*b^4*c^3}=

$$\frac { a ^ { 3 } \times b ^ { 2 } \times a ^ { 4 } } { c ^ { 2 } \times b ^ { 4 } \times c ^ { 3 } } =$$

Evaluate

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

Solution Steps

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

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

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

$$\frac{a^{7}b^{2}}{c^{5}b^{4}}$$

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

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

Differentiate w.r.t. c

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