Solve frac{7st^{3}}{15v^{3}v^2}*5v^3v/28s^3t^2

$$\frac { 7 s t ^ { 3 } } { 15 v ^ { 3 } v ^ { 2 } } \times \frac { 5 v ^ { 3 } v } { 28 s ^ { 3 } t ^ { 2 } }$$

Evaluate

$$\frac{t}{12vs^{2}}$$

Solution Steps

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

$$\frac{7st^{3}}{15v^{5}}\times \frac{5v^{3}v}{28s^{3}t^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{7st^{3}}{15v^{5}}\times \frac{5v^{4}}{28s^{3}t^{2}}$$

Multiply \frac{7st^{3}}{15v^{5}} times \frac{5v^{4}}{28s^{3}t^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7st^{3}\times 5v^{4}}{15v^{5}\times 28s^{3}t^{2}}$$

Cancel out 5\times 7st^{2}v^{4} in both numerator and denominator.

$$\frac{t}{3\times 4vs^{2}}$$

Multiply 3 and 4 to get 12.

$$\frac{t}{12vs^{2}}$$

Differentiate w.r.t. s

$$-\frac{t}{6vs^{3}}$$