Solve 2p^2/15pq^3div9pq2/52

$$\frac { 2 p ^ { 2 } } { 15 p q ^ { 3 } } \div \frac { 9 p q 2 } { 52 }$$

Evaluate

$$\frac{104}{135q_{2}q^{3}}$$

Solution Steps

Divide \frac{2p^{2}}{15pq^{3}} by \frac{9pq_{2}}{52} by multiplying \frac{2p^{2}}{15pq^{3}} by the reciprocal of \frac{9pq_{2}}{52}.

$$\frac{2p^{2}\times 52}{15pq^{3}\times 9pq_{2}}$$

Cancel out pp in both numerator and denominator.

$$\frac{2\times 52}{9\times 15q_{2}q^{3}}$$

Multiply 2 and 52 to get 104.

$$\frac{104}{9\times 15q_{2}q^{3}}$$

Multiply 9 and 15 to get 135.

$$\frac{104}{135q_{2}q^{3}}$$

Differentiate w.r.t. q

$$-\frac{104}{45q_{2}q^{4}}$$