The expression given is:

\[
a^3b^2c \cdot x \cdot abc^2
\]

Let's simplify this expression step-by-step:

1. Combine like terms by grouping the coefficients and similar variables:
   \[
   a^3b^2c \cdot abc^2x = a^3 \cdot a \cdot b^2 \cdot b \cdot c \cdot c^2 \cdot x
   \]

2. Add the exponents of the like bases:
   - For \(a\): \(a^3 \cdot a = a^{3+1} = a^4\)
   - For \(b\): \(b^2 \cdot b = b^{2+1} = b^3\)
   - For \(c\): \(c \cdot c^2 = c^{1+2} = c^3\)

3. Now, rewrite the expression with the simplified terms:
   \[
   a^4b^3c^3x
   \]

So, the simplified form of the expression \( a^3b^2c \cdot x \cdot abc^2 \) is:

\[
a^4b^3c^3x
\]

Would you like further details or have any questions about the simplification process?

Here are 5 related questions that might help you understand more about this topic:

1. How do you multiply expressions with the same base but different exponents?
2. What are the rules for simplifying algebraic expressions?
3. How would the process change if there were coefficients in front of the variables?
4. What is the importance of exponents in algebraic expressions?
5. How can this simplification method be applied to more complex algebraic expressions?

**Tip:** Always combine like terms and simplify exponents step-by-step to avoid mistakes in algebraic simplification.

Learn how to simplify the algebraic expression a^3b^2c x abc^2 with a detailed step-by-step solution. This problem explores algebraic concepts like exponentiation and the product of powers rule, suitable for students in Grades 8-10.

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