https://file.aiquickdraw.com/mathbot/file/17295810304414oz5a27w.jpg

Let's go through and simplify each of the expressions from the image:

9. \( 3^5 \)  
   \[
   3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243
   \]

10. \( 4^3 \)  
   \[
   4^3 = 4 \times 4 \times 4 = 64
   \]

11. \( 2^4 \)  
   \[
   2^4 = 2 \times 2 \times 2 \times 2 = 16
   \]

12. \( 10^8 \)  
   \[
   10^8 = 100,000,000
   \]

13. \( \left( \frac{2}{3} \right)^3 \)  
   \[
   \left( \frac{2}{3} \right)^3 = \frac{2^3}{3^3} = \frac{8}{27}
   \]

14. \( \left( \frac{1}{2} \right)^4 \)  
   \[
   \left( \frac{1}{2} \right)^4 = \frac{1^4}{2^4} = \frac{1}{16}
   \]

15. \( (0.4)^6 \)  
   \[
   (0.4)^6 = 0.004096
   \]

16. \( 7^4 \)  
   \[
   7^4 = 7 \times 7 \times 7 \times 7 = 2401
   \]

17. \( 20 - 2 \cdot 3^2 \)  
   \[
   3^2 = 9 \quad \text{so}, 20 - 2 \cdot 9 = 20 - 18 = 2
   \]

18. \( 6 + 4 \div 2 + 3 \)  
   \[
   4 \div 2 = 2, \quad \text{so}, 6 + 2 + 3 = 11
   \]

19. \( (6^2 - 3^3) \div 2 \)  
   \[
   6^2 = 36, \quad 3^3 = 27 \quad \text{so}, (36 - 27) \div 2 = 9 \div 2 = 4.5
   \]

20. \( 5 \cdot 2^2 \div 2 + 8 \)  
   \[
   2^2 = 4 \quad \text{so}, 5 \cdot 4 \div 2 + 8 = 20 \div 2 + 8 = 10 + 8 = 18
   \]

21. \( 80 - (4 - 1)^3 \)  
   \[
   (4 - 1)^3 = 3^3 = 27 \quad \text{so}, 80 - 27 = 53
   \]

22. \( 52 + 8^2 - 3(4 - 2) \)  
   \[
   8^2 = 64, \quad 4 - 2 = 2 \quad \text{so}, 52 + 64 - 3(2) = 52 + 64 - 6 = 110
   \]

23. \( \frac{6^4 \div 3^2}{9} \)  
   \[
   6^4 = 1296, \quad 3^2 = 9 \quad \text{so}, \frac{1296 \div 9}{9} = \frac{144}{9} = 16
   \]

24. \( \frac{2 \cdot 7 + 4}{9 \div 3} \)  
   \[
   9 \div 3 = 3 \quad \text{so}, \frac{2 \cdot 7 + 4}{3} = \frac{14 + 4}{3} = \frac{18}{3} = 6
   \]

Would you like a deeper explanation for any of these steps?

Here are five related questions to practice:

1. Simplify \( 5^4 \).
2. Solve \( \left( \frac{3}{5} \right)^2 \).
3. Calculate \( (0.5)^5 \).
4. Simplify \( 8 + 5 \cdot 3 - 2^2 \).
5. Solve \( \left( 9^2 - 6^2 \right) \div 3 \).

**Tip:** Remember, the order of operations follows the rule: **PEMDAS** (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

Simplify the given expressions: 3^5, 4^3, 2^4, 10^8, (2/3)^3, (1/2)^4, (0.4)^6, 7^4, 20 - 2 * 3^2, 6 + 4 ÷ 2 + 3, (6^2 - 3^3) ÷ 2, 5 * 2^2 ÷ 2 + 8, 80 - (4 - 1)^3, 52 + 8^2 - 3(4 - 2), (6^4 ÷ 3^2) / 9, (2 * 7 + 4) / (9 ÷ 3).

Explore how to simplify mathematical expressions with exponents and order of operations. This guide walks through examples such as 3^5, 4^3, (2/3)^3, and multi-step arithmetic expressions using PEMDAS. Perfect for students in Grades 6-8.

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