To multiply the two expressions:

\[
\frac{15a^2}{8ab^3c} \times \frac{4c}{5ab}
\]

### Step 1: Multiply the numerators
The numerators are \(15a^2\) and \(4c\):
\[
15a^2 \times 4c = 60a^2c
\]

### Step 2: Multiply the denominators
The denominators are \(8ab^3c\) and \(5ab\):
\[
8ab^3c \times 5ab = 40a^2b^4c
\]

### Step 3: Combine the results
Now we have:
\[
\frac{60a^2c}{40a^2b^4c}
\]

### Step 4: Simplify
- Cancel \(a^2\) in the numerator and denominator.
- Cancel \(c\) in the numerator and denominator.
- \(60 \div 40 = \frac{3}{2}\).

This leaves us with:
\[
\frac{3}{2b^4}
\]

### Final Answer:
\[
\frac{3}{2b^4}
\]

Would you like more details, or do you have any questions?

Here are some related questions:
1. How do you multiply algebraic fractions?
2. How do you simplify expressions involving variables?
3. What are the common rules for canceling terms in fractions?
4. How do you handle exponents during multiplication?
5. What is the role of factoring in simplifying algebraic fractions?

**Tip**: Always look for common terms in the numerator and denominator to simplify early.

Learn how to multiply and simplify algebraic fractions such as 15a^2/8ab^3c and 4c/5ab with this detailed, step-by-step solution. This problem covers key algebraic concepts, including multiplying fractions and simplifying terms. Suitable for students in Grades 8-10.

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