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.