Solve a^3diva^8

$$a ^ { 3 } \div a ^ { 8 }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$a^{3-8}$$

Subtract 8 from 3.

$$a^{-5}$$

Differentiate w.r.t. a

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

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$-5a^{-5-1}$$

Do the arithmetic.

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