Question

I need help with this problem please

A sheet of paper is cut into 6 same-size parts. Each of the parts is then cut into 6 same-size parts and so on.
a. After the 5th, 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----of the smallest pieces of paper after the 5th cut.
​(Type your answer using exponential​ notation.)

Answer 1

6^5, 6^n

Explanation:

To start we can make a quick table of values to determine a relationship:

cut # | # of pieces of paper

1 | 6

2 | 36

3 | 216

4 | 1296

5 | 7776

a) The relationship, as we can see, is powers of 6. Each time we back the cuts, we get 6 times more pieces. So to get the number of pieces after 5 cuts we can do 6^5. There are 7776 pieces of paper.

b) for the nth cut, we replace 5 with n, so 6^n