The problem in the image can be summarized as follows:

• There is a library with 500 books, each with a thickness of $2^3 \, \text{cm}$.
• The goal is to calculate the total length of the bookshelf needed to store these 500 books.

Step 1: Calculate the thickness of each book

The thickness of each book is given by $2^3 \, \text{cm}$.

$2^3 = 8 \, \text{cm}$

So, the thickness of each book is 8 cm.

Step 2: Calculate the total length of the bookshelf

Since there are 500 books, and each book is 8 cm thick, the total length required for the bookshelf is:

$500 \times 8 \, \text{cm} = 4000 \, \text{cm}$

Step 3: Convert to meters

Since 100 cm = 1 meter, we can convert 4000 cm to meters:

$4000 \, \text{cm} = 4000 \div 100 = 40 \, \text{meters}$

Final Answer:

The total length of the bookshelf needed is 40 meters.

Do you want more details or have any questions?

Here are 5 additional related questions for practice:

1. What would the total length be if the thickness of each book were $2^4 \, \text{cm}$?
2. How many books could fit on a 30-meter-long shelf if each book is 8 cm thick?
3. If the total length of the shelf was 20 meters, how many books could be stored?
4. What would be the total length if there were 1000 books, each with a thickness of 5 cm?
5. If each book had a thickness of $3^2 \, \text{cm}$, how long would the bookshelf be for 300 books?

Tip: When working with exponents, it's useful to memorize basic powers of small numbers to speed up calculations!