To simplify the expression \(a^2 \times a \times b \times c \times a^3 \times a^5 \times b^3 \times c^5\), we need to apply the rules of exponents. When multiplying terms with the same base, we add their exponents. Let's group the terms by their bases:

\[
a^2 \times a \times a^3 \times a^5, \quad b \times b^3, \quad c \times c^5
\]

Now, we add the exponents for each base:

1. **For \(a\):**
   \[
   a^2 \times a \times a^3 \times a^5 = a^{2+1+3+5} = a^{11}
   \]

2. **For \(b\):**
   \[
   b \times b^3 = b^{1+3} = b^4
   \]

3. **For \(c\):**
   \[
   c \times c^5 = c^{1+5} = c^6
   \]

Combining these results, we get the simplified expression:

\[
a^{11} \times b^4 \times c^6
\]

### Final Answer:

\[
a^{11} b^4 c^6
\]

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

### Related Questions:
1. How do you simplify expressions with exponents in division?
2. What is the rule for multiplying exponents with the same base?
3. How do you expand expressions that involve multiple terms with exponents?
4. What happens when you have negative exponents in a multiplication problem?
5. How do you deal with fractional exponents when multiplying terms?

### Tip:
When multiplying terms with exponents, always remember to group the terms by their base and then add their exponents!

a^2 × a × b × c × a^3 × a^5 × b^3 × c^5

Learn how to simplify the algebraic expression a^2 × a × b × c × a^3 × a^5 × b^3 × c^5 by applying the rules of exponents. This step-by-step guide covers key concepts such as the Product of Powers rule, making it perfect for students in Grades 6-8.

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