Solve 8p^2div(-5p)

$$8 p ^ { 2 } \div ( - 5 p )$$

Evaluate

$$-\frac{8p}{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}p^{2}}{\left(-5\right)^{1}p^{1}}$$

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

$$\frac{8^{1}p^{2-1}}{\left(-5\right)^{1}}$$

Subtract 1 from 2.

$$\frac{8^{1}p^{1}}{\left(-5\right)^{1}}$$

Divide 8 by -5.

$$-\frac{8}{5}p^{1}$$

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

$$-\frac{8}{5}p$$

Differentiate w.r.t. p

$$-\frac{8}{5} = -1\frac{3}{5} = -1.6$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$-\frac{8}{5}p^{1-1}$$

Do the arithmetic.

$$-\frac{8}{5}p^{0}$$

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

$$-\frac{8}{5}$$