Solve 8p^6*3p^4/16p^5=

$$\frac { 8 p ^ { 6 } \times 3 p ^ { 4 } } { 16 p ^ { 5 } } =$$

Evaluate

$$\frac{3p^{5}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{8p^{10}\times 3}{16p^{5}}$$

Cancel out 8p^{5} in both numerator and denominator.

$$\frac{3p^{5}}{2}$$

Differentiate w.r.t. p

$$\frac{15p^{4}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{24p^{4}}{16}p^{6-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{3p^{4}}{2}p^{1})$$

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}.

$$\frac{3p^{4}}{2}p^{1-1}$$

Do the arithmetic.

$$\frac{3p^{4}}{2}p^{0}$$

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

$$\frac{3p^{4}}{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

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