Solve p^-8/p^3=

$$\frac { p ^ { - 8 } } { p ^ { 3 } } =$$

Differentiate w.r.t. p

$$-\frac{11}{p^{12}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{-11})$$

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}.

$$-11p^{-11-1}$$

Do the arithmetic.

$$-11p^{-12}$$

Evaluate

$$\frac{1}{p^{11}}$$

Solution Steps

Rewrite p^{3} as p^{-8}p^{11}. Cancel out p^{-8} in both numerator and denominator.

$$\frac{1}{p^{11}}$$