Arectangular area of land is being sold off in a smaller pieces. the total area of the land is 2(15th power) square miles. the pieces being sold are 8(3rd power) square miles in size. how many smaller pieces of land can be sold at the stated size? compute the actual number of pieces.

I've got to tell you what it was about this question that made me stop,
look it over, play with it, and try to answer it:  It was the size of the piece
of land involved . . . 2¹⁵ square miles.  I had a funny feeling about that piece
of land, so I went and looked it up, and sure enough, it was just as I suspected.

Let me put it this way:

-- South Carolina
-- West Virginia
-- Maryland
-- Hawaii
-- Massachusetts
-- Vermont
-- New Hampshire
-- New Jersey
-- Connecticut
-- Delaware
-- Rhode Island
Not one of these 11 states has that much land inside its borders.

-- Panama
-- Ireland
-- Costa Rica
-- Israel
-- Denmark
-- Netherlands
-- Switzerland
-- Taiwan
-- Belgium
-- Haiti
Not one of these 10 countries has that much land in it.

And ALL OF THESE PUT TOGETHER don't add up to that much land:
-- Fiji
-- Kuwait
-- Bahamas
-- Jamaica
-- Lebanon
-- Puerto Rico

But that's what the question says, so that's the way to work it.
It's only math.


How many times does   8³   fit into   2¹⁵  ?

We need to evaluate    2¹⁵ / 8³  .
If the bases were the same, then we could simply subtract the exponents.

Notice that  '8'  is the same thing as  2³ .
So  8³  =  (2³)³  =  2⁹ .

Now the big fraction can be written as    2¹⁵ / 2⁹  and that's   2⁶ .
And there you are.
If you start out with  2¹⁵  square miles of land, and start giving away pieces
of  8³  square miles (slightly more land than Hong Kong) to everyone who
walks by, then by the time only  2 million people have walked by, you'll have
nothing left.

But you'll have the last laugh !  Because you can't move a piece of land,
so all those people will have to live next to each other !

As for the second part of the question (Compute the actual number of pieces.),
I must confess that either it's a bogus question or else I just don't get it.

Since the dimensions of the original rectangle (roughly the same area as Belgium)
are not stated, and the pieces of  8³ square miles aren't even described as being
any particular shape, I don't really see any reason why the chopping up can't be
done in such a way that it results in exactly 2⁶ pieces.  

In  conclusion, I'll offer the wry observation that the only tiny number associated
with this problem is the 5 points.