A sheet of paper is cut into 4 same-size parts. Each of the parts is then cut into 4 same-size parts and so on. a. After the 4th cut, how many of the smallest pieces of paper are there? b. After the nth cut, how many of the smallest pieces of paper are there? a. There are 256 of the smallest pieces of paper after the 4th cut. (Type your answer using exponential notation.) b. There are nothing of the smallest pieces of paper after the nth cut. (Type your answer using exponential notation.)

256 ; 262144

Step-by-step explanation:

Given that :

1 sheet is cut into 4

Each of the 4 is also cut into 4

Let number of cut = n

Using the Recursive geometric sequence relation ;

An = a1 * q^(n-1)

2nd cut :

A2 = 1/4 * (1/4)^(2 - 1)

A2 = 1/4 * 1/4

1/A2 = 1/16

A2 = 16

After the 4th cut ; n = 4 ;

A4 = 1/4 * (1/4)^(4 - 1)

A4 = 1/4 * (1/4)^3

1/A4 = 1/4 * 1/4^3

1 / A4 = 1/4 * 1/64

1/A4 = 1/256

A4 = 256 pieces

For. The 9th cut n = 9

A9 = 1/4 * (1/4)^(9 - 1)

A9 = 1/4 * (1/4)^8

1/A9 = 1/4 * 1/4^8

1 / A9 = 1/4 * 1/65536

1/A9 = 1/262144

A9 = 262144 pieces

The answer is you can fit 18 books on the bookshelf. :)