Solve 5p^4q/3pdiv3p^7/4q

$$\frac { 5 p ^ { 4 } q } { 3 p } \div \frac { 3 p ^ { 7 } } { 4 q }$$

Evaluate

$$\frac{20q^{2}}{9p^{4}}$$

Solution Steps

Divide \frac{5p^{4}q}{3p} by \frac{3p^{7}}{4q} by multiplying \frac{5p^{4}q}{3p} by the reciprocal of \frac{3p^{7}}{4q}.

$$\frac{5p^{4}q\times 4q}{3p\times 3p^{7}}$$

Cancel out pp^{3} in both numerator and denominator.

$$\frac{4\times 5qq}{3\times 3p^{4}}$$

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

$$\frac{4\times 5q^{2}}{3\times 3p^{4}}$$

Multiply 4 and 5 to get 20.

$$\frac{20q^{2}}{3\times 3p^{4}}$$

Multiply 3 and 3 to get 9.

$$\frac{20q^{2}}{9p^{4}}$$

Differentiate w.r.t. q

$$\frac{40q}{9p^{4}}$$