Solve -21p^9q^4/16pq^4/7p^2{q^8/12p{q^4}}

$$\frac{ \frac{ -21 { p }^{ 9 } { q }^{ 4 } }{ 16p { q }^{ 4 } } }{ \frac{ 7 { p }^{ 2 } { q }^{ 8 } }{ 12p { q }^{ 4 } } }$$

Evaluate

$$-\frac{9p^{7}}{4q^{4}}$$

Solution Steps

Divide \frac{-21p^{9}q^{4}}{16pq^{4}} by \frac{7p^{2}q^{8}}{12pq^{4}} by multiplying \frac{-21p^{9}q^{4}}{16pq^{4}} by the reciprocal of \frac{7p^{2}q^{8}}{12pq^{4}}.

$$\frac{-21p^{9}q^{4}\times 12pq^{4}}{16pq^{4}\times 7p^{2}q^{8}}$$

Cancel out 4\times 7pp^{2}q^{4}q^{4} in both numerator and denominator.

$$\frac{-3\times 3pp^{6}}{4q^{4}}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

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

Multiply -3 and 3 to get -9.

$$\frac{-9p^{7}}{4q^{4}}$$

Differentiate w.r.t. q

$$\frac{9p^{7}}{q^{5}}$$