Solve 11a^3b:(-11ab)=

$$11 a ^ { 3 } b : ( - 11 a b ) =$$

Evaluate

$$-a^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{11^{1}a^{3}b^{1}}{\left(-11\right)^{1}a^{1}b^{1}}$$

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

$$\frac{11^{1}}{\left(-11\right)^{1}}a^{3-1}b^{1-1}$$

Subtract 1 from 3.

$$\frac{11^{1}}{\left(-11\right)^{1}}a^{2}b^{1-1}$$

Subtract 1 from 1.

$$\frac{11^{1}}{\left(-11\right)^{1}}a^{2}b^{0}$$

For any number a except 0, a^{0}=1.

$$\frac{11^{1}}{\left(-11\right)^{1}}a^{2}$$

Divide 11 by -11.

$$-a^{2}$$

Differentiate w.r.t. a

$$-2a$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{11b}{-11b}a^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$-2a^{1}$$

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

$$-2a$$