Solve a^frac{4{5}}diva^frac{1{5}}

$$a ^ { \frac { 4 } { 5 } } \div a ^ { \frac { 1 } { 5 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{\frac{4}{5}}}{\sqrt[5]{a}}$$

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

$$a^{\frac{4}{5}-\frac{1}{5}}$$

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

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

Differentiate w.r.t. a

$$\frac{3}{5a^{\frac{2}{5}}}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\frac{3}{5}a^{-\frac{2}{5}}$$