Solve -10p^3b^3div(2p^2b^2)

$$- 10 p ^ { 3 } b ^ { 3 } \div ( 2 p ^ { 2 } b ^ { 2 } )$$

Evaluate

$$-5bp$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-10\right)^{1}p^{3}b^{3}}{2^{1}p^{2}b^{2}}$$

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

$$\frac{\left(-10\right)^{1}}{2^{1}}p^{3-2}b^{3-2}$$

Subtract 2 from 3.

$$\frac{\left(-10\right)^{1}}{2^{1}}p^{1}b^{3-2}$$

Subtract 2 from 3.

$$\frac{\left(-10\right)^{1}}{2^{1}}pb^{1}$$

Divide -10 by 2.

$$-5pb$$

Differentiate w.r.t. p

$$-5b$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\left(-\frac{10b^{3}}{2b^{2}}\right)p^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\left(-5b\right)p^{1})$$

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}.

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

Do the arithmetic.

$$\left(-5b\right)p^{0}$$

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

$$\left(-5b\right)\times 1$$

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

$$-5b$$