# Algebra/Arithmetic/Exponent Answers

Return to Exponents | Arithmetic Exponent Problem Answers | Return to Roots |

## Problem 1[edit]

Answers

Multiply the 4s first | Multiply the 9s first | ||||

343 | |||||

21 | 484 |

## Problem 2[edit]

2.a

2.b

2.c

**Answers**

2.a

2.b

2.c

## Problem 3[edit]

Everybody is born to biological parents. Our parents each had biological parents. We can say that our grandparents are mathematically as the number of our ancestors doubles with each generation we go back.

So:

3.a How many times would 2 be multiplied to determine the number of great grandparents?

3.b How many times would 2 be multiplied to determine the number of great-great grandparents?

3.c How many people would be our 2^{8} ancestors?

Answer:

3.a If our grandparents are the 2^{2} generation, then our great-grandparents are one more back so are 2^{3}.

3.b This means our great-great grandparents are one more generation back so would be our 2^{4} ancestors.

3.c Our 2^{8} ancestors would be people.

## Problem 4[edit]

*Problem from previous page*

Answer

## Problem 5[edit]

You tear a piece of paper in half 5 times. How many scraps of paper are you left with?

Answer

You should have 32, or scraps of paper left over. The general solution is:

, where P is the number of paper scraps and r is the number of times the paper has been torn.

An interesting anecdote related to this problem: it was once commonly believed that a piece of paper could only ever be folded 8 times; thus, when unraveled, the paper could contain at most 256 () sections. However, this was later proven false when Britney Gallivan folded a paper 12 times, and derived a function for the actual number of folds that could occur.