Solve (-18a^2b^2):(-6ab^2)

$$( - 18 a ^ { 2 } b ^ { 2 } ) : ( - 6 a b ^ { 2 } )$$

Evaluate

$$3a$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-18\right)^{1}a^{2}b^{2}}{\left(-6\right)^{1}a^{1}b^{2}}$$

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

$$\frac{\left(-18\right)^{1}}{\left(-6\right)^{1}}a^{2-1}b^{2-2}$$

Subtract 1 from 2.

$$\frac{\left(-18\right)^{1}}{\left(-6\right)^{1}}a^{1}b^{2-2}$$

Subtract 2 from 2.

$$\frac{\left(-18\right)^{1}}{\left(-6\right)^{1}}ab^{0}$$

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

$$\frac{\left(-18\right)^{1}}{\left(-6\right)^{1}}a$$

Divide -18 by -6.

$$3a$$

Differentiate w.r.t. a

$$3$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{18b^{2}}{-6b^{2}}\right)a^{2-1})$$

Do the arithmetic.

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

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}.

$$3a^{1-1}$$

Do the arithmetic.

$$3a^{0}$$

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

$$3\times 1$$

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

$$3$$