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 $2^{-30}$.

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.