https://file.aiquickdraw.com/mathbot/file/1726106816174qjejv1g4.jpg

Let's work through the questions visible in the image:

### 17. \( 7 \times 7 \times 7 \times 7 \)
This can be written as:
- **Exponent form:** \( 7^4 \)

### 18. \( 3 \times 3 \times 3 \times 3 \times 3 \times 3 \)
This can be written as:
- **Exponent form:** \( 3^6 \)

### 19. \( \frac{1}{5} \times \frac{1}{5} \)
This can be written as:
- **Exponent form:** \( \left( \frac{1}{5} \right)^2 \)

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### Problems 20–22 ask to write each expression in expanded form and then calculate the value.

#### 20. \( 7^1 \)
- a. **Expanded form:** \( 7 \)
- b. **Value of the expression:** \( 7 \)

#### 21. \( 5^4 \)
- a. **Expanded form:** \( 5 \times 5 \times 5 \times 5 \)
- b. **Value of the expression:** \( 625 \)

#### 22. \( 7(2)^3 \)
- a. **Expanded form:** \( 7 \times (2 \times 2 \times 2) \)
- b. **Value of the expression:** \( 7 \times 8 = 56 \)

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### Evaluate each expression:

#### 23. \( 2^x \) for \( x = 9 \)
- **Value:** \( 2^9 = 512 \)

#### 24. \( 6n^2 \) for \( n = 3 \)
- **Value:** \( 6(3^2) = 6 \times 9 = 54 \)

#### 25. \( 4s^3 \) for \( s = 5 \)
- **Value:** \( 4(5^3) = 4 \times 125 = 500 \)

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Do you need more details or have any questions?

Here are some related questions:
1. What is the general rule for converting repeated multiplication into exponents?
2. How do you simplify \( (a \times b)^n \) when both \( a \) and \( b \) are raised to the power of \( n \)?
3. What is the formula for the square of a binomial, such as \( (a + b)^2 \)?
4. How can exponents be used in real-world problems, like compound interest?
5. How do negative exponents affect the value of an expression?

**Tip:** Always check your expanded form before calculating the value to ensure all terms are correctly represented!

Evaluate expressions with exponents, expanded form, and calculation of values.

Learn how to write expressions with exponents in expanded form and evaluate their values. This problem set covers exponentiation and multiplication, ideal for students in Grades 6-8. Detailed step-by-step solutions are provided for each problem.

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