Solve p^2*p^3/p^4

$$\frac { p ^ { 2 } \times p ^ { 3 } } { p ^ { 4 } }$$

Evaluate

$$p$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$p^{1}$$

Calculate p to the power of 1 and get p.

$$p$$

Differentiate w.r.t. p

$$1$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{p^{5}}{p^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

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

Calculate p to the power of 1 and get p.

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

The derivative of ax^{n} is nax^{n-1}.

$$p^{1-1}$$

Subtract 1 from 1.

$$p^{0}$$

For any term t except 0, t^{0}=1.

$$1$$