Solve 2a^3b^5/4ab^9

$$\frac { 2 a ^ { 3 } b ^ { 5 } } { 4 a b ^ { 9 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}a^{3}b^{5}}{4^{1}a^{1}b^{9}}$$

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

$$\frac{2^{1}}{4^{1}}a^{3-1}b^{5-9}$$

Subtract 1 from 3.

$$\frac{2^{1}}{4^{1}}a^{2}b^{5-9}$$

Subtract 9 from 5.

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

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

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

Differentiate w.r.t. b

$$-\frac{2a^{2}}{b^{5}}$$