Solve frac{t^frac{3{4}}}{t^frac{1{5}}}

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

Evaluate

$$t^{\frac{11}{20}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{t^{\frac{3}{4}}}{\sqrt[5]{t}}$$

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

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

Subtract \frac{1}{5} from \frac{3}{4} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$t^{\frac{11}{20}}$$

Differentiate w.r.t. t

$$\frac{11}{20t^{\frac{9}{20}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{1}t^{\frac{3}{4}-\frac{1}{5}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t^{\frac{11}{20}})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{11}{20}t^{\frac{11}{20}-1}$$

Do the arithmetic.

$$\frac{11}{20}t^{-\frac{9}{20}}$$