Simplify the Algebraic Fraction: 4a⁵/2a³ Using Exponent Rules

Due to the fact that the numerator and the denominator of the fraction have terms with identical bases, we will begin by applying the law of exponents for the division of terms with identical bases:

$\frac{b^m}{b^n}=b^{m-n}$We begin by applying the formula to the given problem:

$\frac{4a^5}{2a^3}=2\cdot a^{5-3}=2\cdot a^2$In the first step we simplify the numerical part of the fraction. This is simple to do and makes it easier to work with the said fraction.

$\frac{4a^5}{2a^3}=\frac{4}{2}\cdot\frac{a^5}{a^3}=2\cdot a^{5-3}=\ldots$We obtain the following answer:

$2a^2$

$$Therefore, the correct answer is option A.