Question

5. A rectangular area of land is being sold off in smaller pieces. The total area of the land is 2 to the power of 15 square miles. The pieces

being sold are 8³ square miles in size. How many smaller pieces of land can be sold at the stated size? Compute the
actual number of pieces.

Answer 1

To find the number of smaller pieces of land that can be sold at the stated size, divide the total area of the land by the size of each piece. The calculation is 2^15 divided by 8^3, which simplifies to 64.

Step-by-step explanation:

To find the total number of smaller pieces of land that can be sold at the stated size, we need to divide the total area of the land by the size of each piece.

The total area of the land is given as 2^15 square miles.

The size of each piece being sold is 8^3 square miles.

Therefore, the number of pieces can be calculated as:

Number of pieces = Total area of land / Size of each piece = 2^15 / 8^3

When we simplify this calculation, we get:

Number of pieces = 2^15 / 2^9 = 2^6 = 64

So, there can be 64 smaller pieces of land sold at the stated size.

Answer 2

`64 \: pieces`

Step-by-step explanation:

`total \: = {2}^(15) \: square \: miles \\ sold \: = {8}^(3)=({2}^(3))^(3) = {2}^(9)square\:miles`

`{2}^(15) / {2}^(9) = {2}^(6) = 64`