To solve the given expression [tex]\(\frac{a^3 b^5}{a^2 b}\)[/tex], we need to simplify both the numerator and the denominator by using the properties of exponents.
The given expression is:
[tex]\[
\frac{a^3 b^5}{a^2 b}
\][/tex]
Let's break it down step by step:
1. Simplify the [tex]\(a\)[/tex] terms:
- In the numerator, we have [tex]\(a^3\)[/tex].
- In the denominator, we have [tex]\(a^2\)[/tex].
- Using the property of exponents [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex], we can simplify [tex]\(\frac{a^3}{a^2}\)[/tex] as follows:
[tex]\[
\frac{a^3}{a^2} = a^{3-2} = a^1 = a
\][/tex]
2. Simplify the [tex]\(b\)[/tex] terms:
- In the numerator, we have [tex]\(b^5\)[/tex].
- In the denominator, we have [tex]\(b\)[/tex] (which is equivalent to [tex]\(b^1\)[/tex]).
- Using the property of exponents [tex]\(\frac{b^m}{b^n} = b^{m-n}\)[/tex], we can simplify [tex]\(\frac{b^5}{b}\)[/tex] as follows:
[tex]\[
\frac{b^5}{b} = b^{5-1} = b^4
\][/tex]
3. Combine the simplified terms:
- After simplifying both the [tex]\(a\)[/tex] and [tex]\(b\)[/tex] terms, we get:
[tex]\[
a \cdot b^4
\][/tex]
Therefore, the expression [tex]\(\frac{a^3 b^5}{a^2 b}\)[/tex] simplifies to:
[tex]\[
a b^4
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{D}
\][/tex]
