Solve 8r^1/2s^-3/2r^-2s^4

$$\frac { 8 r ^ { 1 / 2 } s ^ { - 3 } } { 2 r ^ { - 2 } s ^ { 4 } }$$

Evaluate

$$\frac{4r^{\frac{5}{2}}}{s^{7}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{4s^{-3}\sqrt{r}}{r^{-2}s^{4}}$$

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

$$\frac{4s^{-3}r^{\frac{5}{2}}}{s^{4}}$$

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

$$\frac{4r^{\frac{5}{2}}}{s^{7}}$$

Differentiate w.r.t. s

$$-\frac{28r^{\frac{5}{2}}}{s^{8}}$$