https://file.aiquickdraw.com/mathbot/file/17267561919054u6y8l2s.jpg

Looking at the uploaded image, the mathematical problems visible appear to relate to scientific notation and exponents. I'll describe and solve the relevant parts based on what I see.

### Problem 4:
The text asks to write the predicted maximum impact of the event in scientific notation. The options provided are:
- (A) \( 5.64 \times 10^6 \) euros
- (B) \( 5.64 \times 10^8 \) euros
- (C) \( 0.564 \times 10^9 \) euros
- (D) \( 5.64 \times 10^7 \) euros

From the context, the most accurate answer seems to be **(A) \( 5.64 \times 10^6 \)** euros. This correctly represents the value given in scientific notation for millions of euros.

### Problem 5:
This problem asks to write **32% of 258.5 million** in scientific notation.

- First, calculate 32% of 258.5 million:
  \[
  32\% \times 258.5 = 0.32 \times 258.5 = 82.72 \text{ million}
  \]
  
- Convert 82.72 million to scientific notation:
  \[
  82.72 \text{ million} = 82.72 \times 10^6 = 8.272 \times 10^7
  \]

Thus, the answer is **\( 8.272 \times 10^7 \)** euros.

### Bottom Problem:
The next visible problem involves simplifying the expression \( \frac{(8^{-3})^5 \times (-1)^{-6}}{2^{-15}} \) and expressing the result as a power of 2.

Let me solve this:

\[
(8^{-3})^5 = 8^{-15} = (2^3)^{-15} = 2^{-45}
\]
\[
(-1)^{-6} = 1 \quad (\text{since } (-1) \text{ to an even power is 1})
\]
\[
\frac{2^{-45}}{2^{-15}} = 2^{-45 + 15} = 2^{-30}
\]

Thus, the simplified form is **\( 2^{-30} \)**.

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Would you like any further details on these solutions or additional questions?

Here are 5 related questions:
1. How do you convert a number into scientific notation?
2. How can percentages be used to calculate parts of a larger number?
3. Why does raising a negative number to an even power result in a positive number?
4. How do you simplify expressions with exponents when dividing like bases?
5. How does the base of a number affect its exponentiation rules?

**Tip:** When working with scientific notation, remember to adjust the decimal point correctly and ensure the exponent reflects the correct scale of the number.

The image includes three mathematical problems related to scientific notation and exponents. The first problem involves converting a predicted economic impact into scientific notation, the second asks to calculate 32% of a given value and convert it into scientific notation, and the third simplifies an expression involving exponents of powers of 2.

Solve problems involving scientific notation, calculating percentages, and simplifying exponents. Learn how to express large numbers in scientific notation and handle exponents in algebraic expressions. These problems are suitable for Grades 8-10.

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