Solve 6a^5b^2/4ab^3

$$\frac { 6 a ^ { 5 } b ^ { 2 } } { 4 a b ^ { 3 } }$$

Evaluate

$$\frac{3a^{4}}{2b}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}a^{5}b^{2}}{4^{1}a^{1}b^{3}}$$

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

$$\frac{6^{1}}{4^{1}}a^{5-1}b^{2-3}$$

Subtract 1 from 5.

$$\frac{6^{1}}{4^{1}}a^{4}b^{2-3}$$

Subtract 3 from 2.

$$\frac{6^{1}}{4^{1}}a^{4}\times \frac{1}{b}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}a^{4}\times \frac{1}{b}$$

Differentiate w.r.t. b

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