Solve p^3divp^13

$$p ^ { 3 } \div p ^ { 13 }$$

Evaluate

$$\frac{1}{p^{10}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{p^{3}}{p^{13}}$$

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

$$p^{3-13}$$

Subtract 13 from 3.

$$p^{-10}$$

Differentiate w.r.t. p

$$-\frac{10}{p^{11}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{1}p^{3-13})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{-10})$$

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}.

$$-10p^{-10-1}$$

Do the arithmetic.

$$-10p^{-11}$$