Solve 2p^2/15pq^2div3p^2q2/52

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

Evaluate

$$\frac{104}{45pq_{2}q^{2}}$$

Solution Steps

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

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

Cancel out pp in both numerator and denominator.

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

Multiply 2 and 52 to get 104.

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

Multiply 3 and 15 to get 45.

$$\frac{104}{45pq_{2}q^{2}}$$

Differentiate w.r.t. q_2

$$-\frac{104}{45p\left(qq_{2}\right)^{2}}$$