Solve 12p^2q^3r^-6/8p^3q{r^-2}

$$\frac{ 12 { p }^{ 2 } { q }^{ 3 } { r }^{ -6 } }{ 8 { p }^{ 3 } q { r }^{ -2 } }$$

Evaluate

$$\frac{3q^{2}}{2pr^{4}}$$

Solution Steps

Cancel out 4qp^{2} in both numerator and denominator.

$$\frac{3r^{-6}q^{2}}{2r^{-2}p}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{3q^{2}}{2pr^{4}}$$

Differentiate w.r.t. r

$$-\frac{6q^{2}}{pr^{5}}$$