Solve frac{r^frac{4{3}}}{r^frac{1{3}}}

$$\frac { r ^ { \frac { 4 } { 3 } } } { r ^ { \frac { 1 } { 3 } } }$$

Evaluate

$$r$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{r^{\frac{4}{3}}}{\sqrt[3]{r}}$$

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

$$r^{\frac{4}{3}-\frac{1}{3}}$$

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

$$r^{1}$$

For any term t, t^{1}=t.

$$r$$

Differentiate w.r.t. r

$$1$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}r}(r^{1})$$

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}.

$$r^{1-1}$$

Do the arithmetic.

$$r^{0}$$

For any term t except 0, t^{0}=1.

$$1$$