Solve p+0/p^5

$$\frac { p + 0 } { p ^ { 5 } }$$

Evaluate

$$\frac{1}{p^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

$$p^{1-5}$$

Subtract 5 from 1.

$$p^{-4}$$

Differentiate w.r.t. p

$$-\frac{4}{p^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{1}{1}p^{1-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{-4})$$

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}.

$$-4p^{-4-1}$$

Do the arithmetic.

$$-4p^{-5}$$