Solve a^2b/c^3d:ac^2/bd^3

$$\frac { a ^ { 2 } b } { c ^ { 3 } d } : \frac { a c ^ { 2 } } { b d ^ { 3 } }$$

Evaluate

$$\frac{a\left(bd\right)^{2}}{c^{5}}$$

Solution Steps

Divide \frac{a^{2}b}{c^{3}d} by \frac{ac^{2}}{bd^{3}} by multiplying \frac{a^{2}b}{c^{3}d} by the reciprocal of \frac{ac^{2}}{bd^{3}}.

$$\frac{a^{2}bbd^{3}}{c^{3}dac^{2}}$$

Cancel out ad in both numerator and denominator.

$$\frac{abbd^{2}}{c^{2}c^{3}}$$

Multiply b and b to get b^{2}.

$$\frac{ab^{2}d^{2}}{c^{2}c^{3}}$$

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

$$\frac{ab^{2}d^{2}}{c^{5}}$$

Differentiate w.r.t. a

$$\frac{\left(bd\right)^{2}}{c^{5}}$$