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The given algebraic fraction is:

\[
\frac{8ab}{c} \div \frac{16ab^2}{c^3}
\]

To simplify this expression, let's follow these steps:

### Step 1: Rewrite the division as multiplication
Division of fractions can be rewritten as multiplication by the reciprocal. So:

\[
\frac{8ab}{c} \div \frac{16ab^2}{c^3} = \frac{8ab}{c} \times \frac{c^3}{16ab^2}
\]

### Step 2: Simplify the expression
Now, simplify the expression:

\[
\frac{8ab}{c} \times \frac{c^3}{16ab^2} = \frac{8ab \cdot c^3}{c \cdot 16ab^2}
\]

### Step 3: Cancel common terms
- \( 8 \) and \( 16 \) simplify to \( \frac{1}{2} \) (since \( 8 \div 16 = 1 \div 2 \)).
- \( ab \) in the numerator and \( ab^2 \) in the denominator simplify to \( \frac{1}{b} \).
- \( c^3 \) in the numerator and \( c \) in the denominator simplify to \( c^2 \) (since \( c^3 \div c = c^2 \)).

So, we are left with:

\[
\frac{c^2}{2b}
\]

### Conclusion:
The simplest form of the expression is:

\[
\boxed{\frac{c^2}{2b}}
\]

This corresponds to option **B**.

---

Would you like a more detailed breakdown, or do you have any questions?

### Related questions:
1. How would you simplify a fraction involving polynomials?
2. Can you explain why division of fractions is rewritten as multiplication by the reciprocal?
3. What other operations can be performed on algebraic fractions?
4. How does canceling common terms in an algebraic fraction work?
5. How do you handle negative exponents in algebraic fractions?

### Tip:
Always look for common factors that can be canceled out when simplifying algebraic expressions!

Given algebraic fraction 8ab/c ÷ 16ab²/c³, what is the simplest form of the expression?

Learn how to simplify the algebraic fraction 8ab/c ÷ 16ab²/c³ with step-by-step explanation. This involves applying division of fractions, exponent rules, and canceling common terms. Suitable for students in Grades 8-10.

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