Solve p*p*p*p*p/p*p

$$\frac { p \cdot p \cdot p \cdot p \cdot p } { p \cdot p }$$

Evaluate

$$p^{3}$$

Solution Steps

Multiply p and p to get p^{2}.

$$\frac{p^{2}ppp}{pp}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Multiply p and p to get p^{2}.

$$\frac{p^{5}}{p^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 5 to get 3.

$$p^{3}$$

Differentiate w.r.t. p

$$3p^{2}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{3}p^{0})$$

For any number a except 0, a^{0}=1.

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

The derivative of a constant term is 0.

$$0$$