Let's break down the expressions and compare them step by step.

Expressions:

1. $2^3 \times 2^2$ on the left, $2^6$ on the right.
2. $2^2 \times 3^2$ on the left, $6^3$ on the right.
3. $2^3 \times 3^2$ on the left, $6^2$ on the right.

Simplification:

1. First expression: $2^3 \times 2^2 = 2^{3+2} = 2^5$ Compare with $2^6$: $2^5 < 2^6$ So, the first comparison is less than ( < ).

2. Second expression: $2^2 \times 3^2 = 4 \times 9 = 36$ Compare with $6^3 = 6 \times 6 \times 6 = 216$: $36 < 216$ So, the second comparison is also less than ( < ).

3. Third expression: $2^3 \times 3^2 = 8 \times 9 = 72$ Compare with $6^2 = 6 \times 6 = 36$: $72 > 36$ So, the third comparison is greater than ( > ).

Final Order:

1. $2^3 \times 2^2 < 2^6$
2. $2^2 \times 3^2 < 6^3$
3. $2^3 \times 3^2 > 6^2$

Let me know if you need further details or have any questions!

Here are 5 related questions for practice:

1. Simplify $2^4 \times 2^3$.
2. Compare $3^4$ and $2^6$ using exponents.
3. What is the value of $4^2 \times 5^2$?
4. Is $2^5 > 3^4$?
5. Compare $7^2 \times 5^2$ with $35^2$.

Tip: Remember that multiplying powers of the same base means you add the exponents!