Solve 5p^8p^2/p^4

$$\frac { 5 p ^ { 8 } p ^ { 2 } } { p ^ { 4 } }$$

Evaluate

$$5p^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{5p^{10}}{p^{4}}$$

Cancel out p^{4} in both numerator and denominator.

$$5p^{6}$$

Differentiate w.r.t. p

$$30p^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{5p^{2}}{1}p^{8-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(5p^{2}p^{4})$$

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}.

$$4\times 5p^{2}p^{4-1}$$

Do the arithmetic.

$$20p^{2}p^{3}$$