Solve frac{10y^{5}v^{7}t^-5}{25y^-2v^5t^-2}

$$\frac { 10 y ^ { 5 } v ^ { 7 } t ^ { - 5 } } { 25 y ^ { - 2 } v ^ { 5 } t ^ { - 2 } }$$

Evaluate

$$\frac{2v^{2}y^{7}}{5t^{3}}$$

Solution Steps

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

$$\frac{2t^{-5}v^{2}y^{5}}{5t^{-2}y^{-2}}$$

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

$$\frac{2t^{-5}v^{2}y^{7}}{5t^{-2}}$$

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

$$\frac{2v^{2}y^{7}}{5t^{3}}$$

Differentiate w.r.t. v

$$\frac{4vy^{7}}{5t^{3}}$$