Solve a^2/3/a^8/3

$$\frac { a ^ { 2 / 3 } } { a ^ { 8 / 3 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{\frac{2}{3}}}{a^{\frac{8}{3}}}$$

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

$$a^{\frac{2}{3}-\frac{8}{3}}$$

Subtract \frac{8}{3} from \frac{2}{3} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$a^{-2}$$

Differentiate w.r.t. a

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{\frac{2}{3}-\frac{8}{3}})$$

Do the arithmetic.

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

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}.

$$-2a^{-2-1}$$

Do the arithmetic.

$$-2a^{-3}$$