Solve frac{{a}^frac{1{2}}}{{a}^frac{2{5}}}

$$\frac{ { a }^{ \frac{ 1 }{ 2 } } }{ { a }^{ \frac{ 2 }{ 5 } } }$$

Evaluate

$$\sqrt[10]{a}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$a^{\frac{1}{2}-\frac{2}{5}}$$

Subtract \frac{2}{5} from \frac{1}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\sqrt[10]{a}$$

Differentiate w.r.t. a

$$\frac{1}{10a^{\frac{9}{10}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{\frac{1}{2}-\frac{2}{5}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\sqrt[10]{a})$$

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}.

$$\frac{1}{10}a^{\frac{1}{10}-1}$$

Do the arithmetic.

$$\frac{1}{10}a^{-\frac{9}{10}}$$