Solve 15a^3b^2/20ab^4

$$\frac { 15 a ^ { 3 } b ^ { 2 } } { 20 a b ^ { 4 } }$$

Evaluate

$$\frac{3\times \left(\frac{a}{b}\right)^{2}}{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}a^{3}b^{2}}{20^{1}a^{1}b^{4}}$$

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

$$\frac{15^{1}}{20^{1}}a^{3-1}b^{2-4}$$

Subtract 1 from 3.

$$\frac{15^{1}}{20^{1}}a^{2}b^{2-4}$$

Subtract 4 from 2.

$$\frac{15^{1}}{20^{1}}a^{2}b^{-2}$$

Reduce the fraction \frac{15}{20} to lowest terms by extracting and canceling out 5.

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

Differentiate w.r.t. b

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