Solve -36t^8v^10/12t^6v^5

$$\frac { - 36 t ^ { 8 } v ^ { 10 } } { 12 t ^ { 6 } v ^ { 5 } }$$

Evaluate

$$-3t^{2}v^{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-36\right)^{1}t^{8}v^{10}}{12^{1}t^{6}v^{5}}$$

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

$$\frac{\left(-36\right)^{1}}{12^{1}}t^{8-6}v^{10-5}$$

Subtract 6 from 8.

$$\frac{\left(-36\right)^{1}}{12^{1}}t^{2}v^{10-5}$$

Subtract 5 from 10.

$$\frac{\left(-36\right)^{1}}{12^{1}}t^{2}v^{5}$$

Divide -36 by 12.

$$-3t^{2}v^{5}$$

Differentiate w.r.t. v

$$-15t^{2}v^{4}$$