Solve -12a^6b^6/-3a^2b^4

$$\frac { - 12 a ^ { 6 } b ^ { 6 } } { - 3 a ^ { 2 } b ^ { 4 } }$$

Evaluate

$$4b^{2}a^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from 6.

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

Subtract 4 from 6.

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

Divide -12 by -3.

$$4a^{4}b^{2}$$

Differentiate w.r.t. a

$$16b^{2}a^{3}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4b^{2}a^{4})$$

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}.

$$4\times 4b^{2}a^{4-1}$$

Do the arithmetic.

$$16b^{2}a^{3}$$