Solve 8p^5*4p^7/16p^2

$$\frac { 8 p ^ { 5 } \times 4 p ^ { 7 } } { 16 p ^ { 2 } }$$

Evaluate

$$2p^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$\frac{8p^{12}\times 4}{16p^{2}}$$

Cancel out 2\times 8p^{2} in both numerator and denominator.

$$2p^{10}$$

Differentiate w.r.t. p

$$20p^{9}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{32p^{7}}{16}p^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(2p^{7}p^{3})$$

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}.

$$3\times 2p^{7}p^{3-1}$$

Do the arithmetic.

$$6p^{7}p^{2}$$