Solve 2a^4b^3/4a^8b^4=

$$\frac { 2 a ^ { 4 } b ^ { 3 } } { 4 a ^ { 8 } b ^ { 4 } } =$$

Evaluate

$$\frac{1}{2ba^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{1}a^{4}b^{3}}{4^{1}a^{8}b^{4}}$$

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

$$\frac{2^{1}}{4^{1}}a^{4-8}b^{3-4}$$

Subtract 8 from 4.

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

Subtract 4 from 3.

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

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

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

Differentiate w.r.t. b

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