Solve (5^5*p^7)div(25*p^3)

$$( 5 ^ { 5 } \times p ^ { 7 } ) \div ( 25 \times p ^ { 3 } )$$

Evaluate

$$125p^{4}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{5^{5}p^{7}}{25^{1}p^{3}}$$

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

$$\frac{5^{5}p^{7-3}}{25^{1}}$$

Subtract 3 from 7.

$$\frac{5^{5}p^{4}}{25^{1}}$$

Raise 5 to the power 5.

$$\frac{3125p^{4}}{25^{1}}$$

Divide 3125 by 25.

$$125p^{4}$$

Differentiate w.r.t. p

$$500p^{3}$$

Steps Using Definition of a Derivative

Cancel out p^{3} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{5^{5}p^{4}}{25})$$

Calculate 5 to the power of 5 and get 3125.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{3125p^{4}}{25})$$

Divide 3125p^{4} by 25 to get 125p^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}p}(125p^{4})$$

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

$$4\times 125p^{4-1}$$

Multiply 4 times 125.

$$500p^{4-1}$$

Subtract 1 from 4.

$$500p^{3}$$