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Let's simplify the given expression step by step:

The expression is:

\[
\frac{3p^2 \times 2p}{12p^2}
\]

### Step 1: Multiply the terms in the numerator
\[
3p^2 \times 2p = 6p^3
\]

Now the expression becomes:
\[
\frac{6p^3}{12p^2}
\]

### Step 2: Simplify the fraction
Simplify the constants:
\[
\frac{6}{12} = \frac{1}{2}
\]

Now simplify the powers of \(p\):
\[
\frac{p^3}{p^2} = p^{3-2} = p
\]

So, the expression simplifies to:
\[
\frac{p}{2}
\]

### Final Answer:
The correct option is \( \frac{p}{2} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you simplify expressions with variables and exponents?
2. What is the rule for dividing terms with the same base but different exponents?
3. How do you identify common factors in a fraction?
4. How does simplifying fractions with variables differ from simplifying numeric fractions?
5. Can you explain why we subtract exponents when dividing like bases?

**Tip:** When simplifying expressions with exponents, remember to subtract the powers when dividing terms with the same base.

Learn how to fully simplify the algebraic expression (3p^2 × 2p) / 12p^2 using the laws of exponents and fraction simplification techniques. This detailed solution covers key algebraic concepts and is suitable for students in Grades 8-10.

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