https://file.aiquickdraw.com/mathbot/file/1727721144414d6oi3wnl.jpg

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!

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

Learn how to compare expressions involving exponents. Compare 2^3 × 2^2 with 2^6, 2^2 × 3^2 with 6^3, and 2^3 × 3^2 with 6^2. This problem focuses on exponentiation and the properties of exponents, suitable for Grades 6-8 students.

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