Solve frac{12a^{3}b^{6}}{5c^2d^3}div8b^2/3ad*10c^3d/9a

$$\frac { 12 a ^ { 3 } b ^ { 6 } } { 5 c ^ { 2 } d ^ { 3 } } \div \frac { 8 b ^ { 2 } } { 3 a d } \times \frac { 10 c ^ { 3 } d } { 9 a }$$

Evaluate

$$\frac{ca^{3}b^{4}}{d}$$

Solution Steps

Divide \frac{12a^{3}b^{6}}{5c^{2}d^{3}} by \frac{8b^{2}}{3ad} by multiplying \frac{12a^{3}b^{6}}{5c^{2}d^{3}} by the reciprocal of \frac{8b^{2}}{3ad}.

$$\frac{12a^{3}b^{6}\times 3ad}{5c^{2}d^{3}\times 8b^{2}}\times \frac{10c^{3}d}{9a}$$

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

$$\frac{3\times 3aa^{3}b^{4}}{2\times 5c^{2}d^{2}}\times \frac{10c^{3}d}{9a}$$

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

$$\frac{3\times 3a^{4}b^{4}}{2\times 5c^{2}d^{2}}\times \frac{10c^{3}d}{9a}$$

Multiply 3 and 3 to get 9.

$$\frac{9a^{4}b^{4}}{2\times 5c^{2}d^{2}}\times \frac{10c^{3}d}{9a}$$

Multiply 2 and 5 to get 10.

$$\frac{9a^{4}b^{4}}{10c^{2}d^{2}}\times \frac{10c^{3}d}{9a}$$

Multiply \frac{9a^{4}b^{4}}{10c^{2}d^{2}} times \frac{10c^{3}d}{9a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9a^{4}b^{4}\times 10c^{3}d}{10c^{2}d^{2}\times 9a}$$

Cancel out 9\times 10adc^{2} in both numerator and denominator.

$$\frac{ca^{3}b^{4}}{d}$$

Differentiate w.r.t. b

$$\frac{4c\left(ab\right)^{3}}{d}$$