Solve -3a^5b/-12a^3b^2?

$$\frac { - 3 a ^ { 5 } b } { - 12 a ^ { 3 } b ^ { 2 } } ?$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-3\right)^{1}a^{5}b^{1}}{\left(-12\right)^{1}a^{3}b^{2}}$$

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

$$\frac{\left(-3\right)^{1}}{\left(-12\right)^{1}}a^{5-3}b^{1-2}$$

Subtract 3 from 5.

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

Subtract 2 from 1.

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

Reduce the fraction \frac{-3}{-12} to lowest terms by extracting and canceling out 3.

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

Differentiate w.r.t. b

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