Solve 5c^2d/4ab^2div3d/2abc

$$\frac { 5 c ^ { 2 } d } { 4 a b ^ { 2 } } \div \frac { 3 d } { 2 a b c }$$

Evaluate

$$\frac{5c^{3}}{6b}$$

Solution Steps

Divide \frac{5c^{2}d}{4ab^{2}} by \frac{3d}{2abc} by multiplying \frac{5c^{2}d}{4ab^{2}} by the reciprocal of \frac{3d}{2abc}.

$$\frac{5c^{2}d\times 2abc}{4ab^{2}\times 3d}$$

Cancel out 2abd in both numerator and denominator.

$$\frac{5cc^{2}}{2\times 3b}$$

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

$$\frac{5c^{3}}{2\times 3b}$$

Multiply 2 and 3 to get 6.

$$\frac{5c^{3}}{6b}$$

Differentiate w.r.t. b

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