Solve (+14a^3b^2):(-7ab)=

$$( + 14 a ^ { 3 } b ^ { 2 } ) : ( - 7 a b ) =$$

Evaluate

$$-2ba^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{14^{1}a^{3}b^{2}}{\left(-7\right)^{1}a^{1}b^{1}}$$

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

$$\frac{14^{1}}{\left(-7\right)^{1}}a^{3-1}b^{2-1}$$

Subtract 1 from 3.

$$\frac{14^{1}}{\left(-7\right)^{1}}a^{2}b^{2-1}$$

Subtract 1 from 2.

$$\frac{14^{1}}{\left(-7\right)^{1}}a^{2}b^{1}$$

Divide 14 by -7.

$$-2a^{2}b$$

Differentiate w.r.t. a

$$-4ab$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{14b^{2}}{-7b}a^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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

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

$$\left(-4b\right)a$$