Solve 8a^2b^3div(-2ab)=?

$$8 a ^ { 2 } b ^ { 3 } \div ( - 2 a b ) = ?$$

Evaluate

$$-4ab^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{8^{1}a^{2}b^{3}}{\left(-2\right)^{1}a^{1}b^{1}}$$

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

$$\frac{8^{1}}{\left(-2\right)^{1}}a^{2-1}b^{3-1}$$

Subtract 1 from 2.

$$\frac{8^{1}}{\left(-2\right)^{1}}a^{1}b^{3-1}$$

Subtract 1 from 3.

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

Divide 8 by -2.

$$-4ab^{2}$$

Differentiate w.r.t. a

$$-4b^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8b^{3}}{-2b}a^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-4b^{2}\right)a^{1})$$

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}.

$$\left(-4b^{2}\right)a^{1-1}$$

Do the arithmetic.

$$\left(-4b^{2}\right)a^{0}$$

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

$$\left(-4b^{2}\right)\times 1$$

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

$$-4b^{2}$$