Solve a^3:a^6

$$a ^ { 3 } : a ^ { 6 }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{a^{3}}{a^{6}}$$

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

$$a^{3-6}$$

Subtract 6 from 3.

$$a^{-3}$$

Differentiate w.r.t. a

$$-\frac{3}{a^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{1}a^{3-6})$$

Do the arithmetic.

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

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}.

$$-3a^{-3-1}$$

Do the arithmetic.

$$-3a^{-4}$$