Solve 10p^4/6p

$$\frac { 10 p ^ { 4 } } { 6 p }$$

Evaluate

$$\frac{5p^{3}}{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}p^{4}}{6^{1}p^{1}}$$

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

$$\frac{10^{1}p^{4-1}}{6^{1}}$$

Subtract 1 from 4.

$$\frac{10^{1}p^{3}}{6^{1}}$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{3}p^{3}$$

Differentiate w.r.t. p

$$5p^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{10}{6}p^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{5}{3}p^{3})$$

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}.

$$3\times \frac{5}{3}p^{3-1}$$

Do the arithmetic.

$$5p^{2}$$