https://file.aiquickdraw.com/mathbot/file/1725555350241n56ig2un.jpg

Let's break down and solve each problem shown in the image.

### 1. Solve: 
\[
2^{-3} \times (6 \div 3) - 4^2
\]

- \( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} \)
- \( 6 \div 3 = 2 \)
- So, we now have:
  \[
  \frac{1}{8} \times 2 - 4^2 = \frac{1}{8} \times 2 - 16
  \]
  \[
  = \frac{2}{8} - 16 = \frac{1}{4} - 16
  \]
  Convert 16 into a fraction:
  \[
  \frac{1}{4} - 16 = \frac{1}{4} - \frac{64}{4} = \frac{1 - 64}{4} = \frac{-63}{4}
  \]
  Final answer: \( \frac{-63}{4} \) or -15.75.

### 2. Convert \( 19.2 \times 10^8 \) minutes to hours.
Since 1 hour = 60 minutes, we divide the minutes by 60:
\[
\frac{19.2 \times 10^8}{60} = 0.32 \times 10^8 = 3.2 \times 10^7 \text{ hours}
\]

The correct answer is option **(b) \( 3.2 \times 10^7 \) hours**.

### 3. Trash problem:
Given:
- The average person throws away \( 4.5 \times 10^2 \) grams of trash per day.
- There were \( 3.2 \times 10^8 \) people in the U.S. in 2013.

To find how much trash was thrown away per year:
\[
\text{Daily trash} = 4.5 \times 10^2 \times 3.2 \times 10^8 = 1.44 \times 10^{11} \text{ grams per day}
\]
Now, for the whole year (365 days):
\[
1.44 \times 10^{11} \times 365 = 5.256 \times 10^{13} \text{ grams per year}
\]

This is the total trash in grams thrown away in 2013.

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Would you like more details on any of these solutions or further explanations?

Here are five related questions to deepen your understanding:
1. How would the result in question 1 change if the exponent of 2 was different?
2. How do scientific notation conversions help in large data sets like in question 2?
3. What is the significance of unit conversions in real-life scenarios?
4. Can you solve a similar problem to question 3, but for different countries or years?
5. What are some other mathematical applications of scientific notation?

**Tip**: When converting units or solving exponential problems, breaking down the problem into smaller steps simplifies the calculations.

1) Solve: 2^{-3} × (6 ÷ 3) - 4^2. 2) Convert 19.2 × 10^8 minutes to hours. 3) Calculate the trash produced in the US using given data on grams of trash per person and the US population.

This page explains how to solve problems involving exponents, scientific notation, and unit conversions. Learn how to calculate values like 2^{-3} × (6 ÷ 3) - 4^2, convert 19.2 × 10^8 minutes to hours, and compute the trash produced in the US based on population data.

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