Solve p^3/p^6

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

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$p^{3-6}$$

Subtract 6 from 3.

$$p^{-3}$$

Differentiate w.r.t. p

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

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$-3p^{-3-1}$$

Do the arithmetic.

$$-3p^{-4}$$