Solve 12a^2b^2/2ab^3

$$\frac { 12 a ^ { 2 } b ^ { 2 } } { 2 a b ^ { 3 } }$$

Evaluate

$$\frac{6a}{b}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}a^{2}b^{2}}{2^{1}a^{1}b^{3}}$$

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

$$\frac{12^{1}}{2^{1}}a^{2-1}b^{2-3}$$

Subtract 1 from 2.

$$\frac{12^{1}}{2^{1}}a^{1}b^{2-3}$$

Subtract 3 from 2.

$$\frac{12^{1}}{2^{1}}a\times \frac{1}{b}$$

Divide 12 by 2.

$$6a\times \frac{1}{b}$$

Differentiate w.r.t. a

$$\frac{6}{b}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{12b^{2}}{2b^{3}}a^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{6}{b}a^{1})$$

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}.

$$\frac{6}{b}a^{1-1}$$

Do the arithmetic.

$$\frac{6}{b}a^{0}$$

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

$$\frac{6}{b}\times 1$$

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

$$\frac{6}{b}$$