To simplify the given expression [tex]\(\frac{a^3 b^5}{a^4 b}\)[/tex], we need to apply the rules of exponents, which state that [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex] and [tex]\(\frac{b^m}{b^n} = b^{m-n}\)[/tex].
Let's simplify the numerator and the denominator separately:
1. Simplifying the [tex]\(a\)[/tex] terms:
[tex]\[
\frac{a^3}{a^4} = a^{3-4} = a^{-1} = \frac{1}{a}
\][/tex]
2. Simplifying the [tex]\(b\)[/tex] terms:
[tex]\[
\frac{b^5}{b} = b^{5-1} = b^4
\][/tex]
Combining these simplified parts, we get:
[tex]\[
\frac{a^3 b^5}{a^4 b} = \left( \frac{1}{a} \right) \left( b^4 \right) = \frac{b^4}{a}
\][/tex]
Thus, the simplified expression is:
[tex]\[
\frac{b^4}{a}
\][/tex]
Therefore, the correct answer is:
A. [tex]\(\frac{b^4}{a}\)[/tex]
