Solve 4a^2b^5/8a^6b^2

$$\frac { 4 a ^ { 2 } b ^ { 5 } } { 8 a ^ { 6 } b ^ { 2 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}a^{2}b^{5}}{8^{1}a^{6}b^{2}}$$

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

$$\frac{4^{1}}{8^{1}}a^{2-6}b^{5-2}$$

Subtract 6 from 2.

$$\frac{4^{1}}{8^{1}}a^{-4}b^{5-2}$$

Subtract 2 from 5.

$$\frac{4^{1}}{8^{1}}\times \frac{1}{a^{4}}b^{3}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

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

Differentiate w.r.t. b

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