Question

A rectangular area of land is being sold off in smaller pieces. The total area of the land is 2^15 square miles. The pieces being sold are 8^3 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

Answer:

64

Step-by-step explanation:

We have been given that the total area of the land is 2^15 square miles. The pieces being sold are 8^3 square miles in size.

The number of smaller pieces of land will the quotient of total area and area of each small piece.

$\text{Number of smaller pieces of land}=\frac{2^{15}}{8^3}$

We can rewrite $8^3$ as $8^3=(2^3)^3=2^{3*3}=2^9$

$\text{Number of smaller pieces of land}=\frac{2^{15}}{2^9}$

Using quotient property of exponents, we will get:

$\text{Number of smaller pieces of land}=2^{15-9}$

$\text{Number of smaller pieces of land}=2^{6}$

$\text{Number of smaller pieces of land}=64$

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

Answer 2

Total area of the rectangular land = 2^15 sq. miles
                                                     = 32768 sq. miles

total area of the pieces being sold = 8^3 sq. miles
                                                       = 512 sq. miles

now total no. of pieces = total area of the land / the area of samaller land that's                                                                                     being sold
                                     = 32768 / 512
                                     = 64

so the actual number of pieces is 64