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The question asks to order three mathematical expressions using either the symbols \( > \), \( < \), or \( = \).

The expressions involve exponents:

1. \( 2^2 \times 3 \) vs. \( 6^2 \)
2. \( 2^3 \times 3^2 \) vs. \( 6^2 \)
3. \( 2^5 \times 3 \) vs. \( 6^3 \)

Let’s calculate each side for comparison:

### 1. \( 2^2 \times 3 \) vs. \( 6^2 \)
- \( 2^2 = 4 \)
- \( 4 \times 3 = 12 \)
- \( 6^2 = 36 \)

So, \( 12 < 36 \).

### 2. \( 2^3 \times 3^2 \) vs. \( 6^2 \)
- \( 2^3 = 8 \)
- \( 3^2 = 9 \)
- \( 8 \times 9 = 72 \)
- \( 6^2 = 36 \)

So, \( 72 > 36 \).

### 3. \( 2^5 \times 3 \) vs. \( 6^3 \)
- \( 2^5 = 32 \)
- \( 32 \times 3 = 96 \)
- \( 6^3 = 216 \)

So, \( 96 < 216 \).

### Final Order:
- \( 2^2 \times 3 < 6^2 \)
- \( 2^3 \times 3^2 > 6^2 \)
- \( 2^5 \times 3 < 6^3 \)

You can use the symbols \( <, >, < \) in the correct order.

Would you like more details or have any questions? Here are some related questions:

1. How do we simplify expressions with exponents?
2. Why does \( 2^3 \times 3^2 \) result in a value greater than \( 6^2 \)?
3. What is the general rule for comparing powers of different numbers?
4. How does multiplying bases affect the result compared to raising the base to a power?
5. Can exponents always be compared directly?

**Tip:** When comparing exponential expressions, simplify both sides to numerical values for direct comparison.

Order the expressions by choosing >, <, or =: 1. 2^2 × 3 vs. 6^2, 2. 2^3 × 3^2 vs. 6^2, 3. 2^5 × 3 vs. 6^3.

Order exponential expressions using >, <, or =: (1) 2^2 × 3 vs. 6^2, (2) 2^3 × 3^2 vs. 6^2, (3) 2^5 × 3 vs. 6^3. Learn how to compare exponential expressions and powers in this step-by-step guide.

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