Solve (-3a^2b^4):(+2ab)

$$( - 3 a ^ { 2 } b ^ { 4 } ) : ( + 2 a b )$$

Evaluate

$$-\frac{3ab^{3}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-3\right)^{1}a^{2}b^{4}}{2^{1}a^{1}b^{1}}$$

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

$$\frac{\left(-3\right)^{1}}{2^{1}}a^{2-1}b^{4-1}$$

Subtract 1 from 2.

$$\frac{\left(-3\right)^{1}}{2^{1}}a^{1}b^{4-1}$$

Subtract 1 from 4.

$$\frac{\left(-3\right)^{1}}{2^{1}}ab^{3}$$

Divide -3 by 2.

$$-\frac{3}{2}ab^{3}$$

Differentiate w.r.t. a

$$-\frac{3b^{3}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{3b^{4}}{2b}\right)a^{2-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-\frac{3b^{3}}{2}\right)a^{0}$$

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

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

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

$$-\frac{3b^{3}}{2}$$