Question: Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
$$\frac{a^3b^5}{a^4b}$$
a^3b^5
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a^4b
b^4
---
a
a
--
b^3
1
--
ab^4
ab^4
1. **State the problem:** Simplify the expression $$\frac{a^3b^5}{a^4b}$$ to find an equivalent expression.
2. **Recall the laws of exponents:**
- When dividing like bases, subtract the exponents: $$\frac{x^m}{x^n} = x^{m-n}$$.
- Apply this rule separately to the variables $$a$$ and $$b$$.
3. **Apply the exponent rule to $$a$$:**
$$\frac{a^3}{a^4} = a^{3-4} = a^{-1} = \frac{1}{a}$$.
4. **Apply the exponent rule to $$b$$:**
$$\frac{b^5}{b^1} = b^{5-1} = b^4$$.
5. **Combine the simplified parts:**
$$\frac{a^3b^5}{a^4b} = a^{-1}b^4 = \frac{b^4}{a}$$.
6. **Final answer:**
$$\boxed{\frac{b^4}{a}}$$ is equivalent to the original expression.
This matches the second answer choice.