Solve 2s/5t*25s^2/12t

$$\frac { 2 s } { 5 t } \cdot \frac { 25 s ^ { 2 } } { 12 t }$$

Evaluate

$$\frac{5s^{3}}{6t^{2}}$$

Solution Steps

Multiply \frac{2s}{5t} times \frac{25s^{2}}{12t} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2s\times 25s^{2}}{5t\times 12t}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{5ss^{2}}{6tt}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{5s^{3}}{6tt}$$

Multiply t and t to get t^{2}.

$$\frac{5s^{3}}{6t^{2}}$$

Differentiate w.r.t. s

$$\frac{5\times \left(\frac{s}{t}\right)^{2}}{2}$$