Solve frac{4a^{2}b^{-6}}{d^{2}c^{-4}}*d^3c^3/12a^3b^-8

$$\frac { 4 a ^ { 2 } b ^ { - 6 } } { d ^ { 2 } c ^ { - 4 } } \cdot \frac { d ^ { 3 } c ^ { 3 } } { 12 a ^ { 3 } b ^ { - 8 } }$$

Evaluate

$$\frac{db^{2}c^{7}}{3a}$$

Solution Steps

Multiply \frac{4a^{2}b^{-6}}{d^{2}c^{-4}} times \frac{d^{3}c^{3}}{12a^{3}b^{-8}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4a^{2}b^{-6}d^{3}c^{3}}{d^{2}c^{-4}\times 12a^{3}b^{-8}}$$

Cancel out 4a^{2}d^{2} in both numerator and denominator.

$$\frac{b^{-6}dc^{3}}{3b^{-8}c^{-4}a}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{db^{2}c^{7}}{3a}$$

Differentiate w.r.t. c

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