Solve frac{frac{4r^{3}s}{t^5}}{2s^7/r^2t^9}

$$\frac { \frac { 4 r ^ { 3 } s } { t ^ { 5 } } } { \frac { 2 s ^ { 7 } } { r ^ { 2 } t ^ { 9 } } }$$

Evaluate

$$\frac{2t^{4}r^{5}}{s^{6}}$$

Solution Steps

Divide \frac{4r^{3}s}{t^{5}} by \frac{2s^{7}}{r^{2}t^{9}} by multiplying \frac{4r^{3}s}{t^{5}} by the reciprocal of \frac{2s^{7}}{r^{2}t^{9}}.

$$\frac{4r^{3}sr^{2}t^{9}}{t^{5}\times 2s^{7}}$$

Cancel out 2st^{5} in both numerator and denominator.

$$\frac{2r^{2}r^{3}t^{4}}{s^{6}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{2r^{5}t^{4}}{s^{6}}$$

Differentiate w.r.t. t

$$\frac{8t^{3}r^{5}}{s^{6}}$$