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

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

Evaluate

$$\frac{4a}{b}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from 3.

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

Subtract 3 from 2.

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

Divide 12 by 3.

$$4a\times \frac{1}{b}$$

Differentiate w.r.t. b

$$-\frac{4a}{b^{2}}$$