Solve a^6/a^frac{5{6}}

$$\frac { a ^ { 6 } } { a ^ { \frac { 5 } { 6 } } }$$

Evaluate

$$a^{\frac{31}{6}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{6}}{a^{\frac{5}{6}}}$$

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

$$a^{6-\frac{5}{6}}$$

Subtract \frac{5}{6} from 6.

$$a^{\frac{31}{6}}$$

Differentiate w.r.t. a

$$\frac{31a^{\frac{25}{6}}}{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{6-\frac{5}{6}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{31}{6}})$$

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}.

$$\frac{31}{6}a^{\frac{31}{6}-1}$$

Do the arithmetic.

$$\frac{31}{6}a^{\frac{25}{6}}$$