Algebra/Arithmetic/Exponent Answers

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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 28 ancestors?

Answer:

3.a If our grandparents are the 22 generation, then our great-grandparents are one more back so are 23. 
3.b This means our great-great grandparents are one more generation back so would be our 24 ancestors.
3.c Our 28 ancestors would be  people.

Problem 4[edit]

4.a Identify the square numbers between 50 and 100
4.b Identify the square numbers between 160 and 200.

Answer

4.a We know that 102 = 100 so any larger number is out of the range. 
So 92 = 81 in the range
82 = 64 in the range
72 = 49 too small for the range.

So the square numbers in the range are 64, 81 and 100.

4.b 122 = 144 and is too small for our range
132 = 169 is in the range
142 = 196 is in the range, and the next square will be too large.

So the square numbers in this range are 169 and 196

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.