Solve frac{a^frac{5{3}}}{a^frac{1{3}}}

$$\frac { a ^ { \frac { 5 } { 3 } } } { a ^ { \frac { 1 } { 3 } } }$$

Evaluate

$$a^{\frac{4}{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{\frac{5}{3}}}{\sqrt[3]{a}}$$

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

$$a^{\frac{5}{3}-\frac{1}{3}}$$

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

$$a^{\frac{4}{3}}$$

Differentiate w.r.t. a

$$\frac{4\sqrt[3]{a}}{3}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{4}{3}})$$

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}.

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

Do the arithmetic.

$$\frac{4}{3}\sqrt[3]{a}$$