https://file.aiquickdraw.com/mathbot/file/1726098752234lydkswfc.jpg

Let's go through the problems one by one from the image you've provided.

### 3. Evaluate each power.

a) \( 3^2 = 3 \times 3 = 9 \)

b) \( 4^3 = 4 \times 4 \times 4 = 64 \)

c) \( 2^8 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 256 \)

d) \( 5^4 = 5 \times 5 \times 5 \times 5 = 625 \)

e) \( 1^6 = 1 \times 1 \times 1 \times 1 \times 1 \times 1 = 1 \)

f) \( 10^4 = 10 \times 10 \times 10 \times 10 = 10,000 \)

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### 4. Area and square roots.

a)  
- Area: \( 2 \times 2 = 4 \) square units  
- \( \sqrt{4} = 2 \)

b)  
- Area: \( 6 \times 6 = 36 \) square units  
- \( \sqrt{36} = 6 \)

c)  
- Area: \( 3 \times 3 = 9 \) square units  
- \( \sqrt{9} = 3 \)

d)  
- Area: \( 7 \times 7 = 49 \) square units  
- \( \sqrt{49} = 7 \)

e)  
- Area: \( 4 \times 4 = 16 \) square units  
- \( \sqrt{16} = 4 \)

f)  
- Area: \( 5 \times 5 = 25 \) square units  
- \( \sqrt{25} = 5 \)

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### 5. Calculate each square root.

a) \( \sqrt{100} = 10 \)

b) \( \sqrt{81} = 9 \)

c) \( \sqrt{64} = 8 \)

d) \( \sqrt{10,000} = 100 \)

e) \( \sqrt{144} = 12 \)

f) \( \sqrt{121} = 11 \)

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If you need more details or further explanations, feel free to ask! Here are five related questions that could expand on this topic:

1. What is the value of \( 2^5 \)?
2. How do you calculate the cube root of a number, such as \( \sqrt[3]{27} \)?
3. Can you find the area and square root for \( 9 \times 9 \)?
4. What are the properties of exponents for \( a^m \times a^n \)?
5. How can square roots be applied to real-world problems?

**Tip:** For large powers, try breaking down the number using known squares or cubes to make the calculation easier.

Learn how to evaluate exponents, calculate square roots, and find the area of squares. This exercise involves powers of numbers, square roots, and area calculations, making it ideal for students in Grades 6-8.

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