Solve 36r^2t^14/24rt^11

$$\frac { 36 r ^ { 2 } t ^ { 14 } } { 24 r t ^ { 11 } }$$

Evaluate

$$\frac{3rt^{3}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{36^{1}r^{2}t^{14}}{24^{1}r^{1}t^{11}}$$

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

$$\frac{36^{1}}{24^{1}}r^{2-1}t^{14-11}$$

Subtract 1 from 2.

$$\frac{36^{1}}{24^{1}}r^{1}t^{14-11}$$

Subtract 11 from 14.

$$\frac{36^{1}}{24^{1}}rt^{3}$$

Reduce the fraction \frac{36}{24} to lowest terms by extracting and canceling out 12.

$$\frac{3}{2}rt^{3}$$

Differentiate w.r.t. t

$$\frac{9rt^{2}}{2}$$