Solve (-12/7a^4b^4):(-6/7a^3b^2)

$$( - \frac { 12 } { 7 } a ^ { 4 } b ^ { 4 } ) : ( - \frac { 6 } { 7 } a ^ { 3 } b ^ { 2 } )$$

Evaluate

$$2ab^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-\frac{12}{7}\right)^{1}a^{4}b^{4}}{\left(-\frac{6}{7}\right)^{1}a^{3}b^{2}}$$

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

$$\frac{\left(-\frac{12}{7}\right)^{1}}{\left(-\frac{6}{7}\right)^{1}}a^{4-3}b^{4-2}$$

Subtract 3 from 4.

$$\frac{\left(-\frac{12}{7}\right)^{1}}{\left(-\frac{6}{7}\right)^{1}}a^{1}b^{4-2}$$

Subtract 2 from 4.

$$\frac{\left(-\frac{12}{7}\right)^{1}}{\left(-\frac{6}{7}\right)^{1}}ab^{2}$$

Divide -\frac{12}{7} by -\frac{6}{7} by multiplying -\frac{12}{7} by the reciprocal of -\frac{6}{7}.

$$2ab^{2}$$

Differentiate w.r.t. a

$$2b^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{\frac{12b^{4}}{7}}{-\frac{6b^{2}}{7}}\right)a^{4-3})$$

Do the arithmetic.

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

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}.

$$2b^{2}a^{1-1}$$

Do the arithmetic.

$$2b^{2}a^{0}$$

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

$$2b^{2}\times 1$$

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

$$2b^{2}$$