Solve b^3t/b^frac{5{6}t^frac{4{3}}}

$$\frac { b ^ { 3 } t } { b ^ { \frac { 5 } { 6 } } t ^ { \frac { 4 } { 3 } } }$$

Evaluate

$$\frac{b^{\frac{13}{6}}}{\sqrt[3]{t}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{b^{3}t^{1}}{b^{\frac{5}{6}}t^{\frac{4}{3}}}$$

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

$$b^{3-\frac{5}{6}}t^{1-\frac{4}{3}}$$

Subtract \frac{5}{6} from 3.

$$b^{\frac{13}{6}}t^{1-\frac{4}{3}}$$

Subtract \frac{4}{3} from 1.

$$b^{\frac{13}{6}}t^{-\frac{1}{3}}$$

Differentiate w.r.t. t

$$-\frac{b^{\frac{13}{6}}}{3t^{\frac{4}{3}}}$$