Algebra/Arithmetic/Exponent Answers

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Problem 1[edit]

  1. 7^3
  2. 5 + 4^2
  3. 1213 - 9^3

Answers

7^3 5 + 4^2 1213 - 9^3
7 \times 7 \times 7 5 + 4 \times 4 1213 - 9 \times 9 \times 9
49 \times 7 Multiply the 4s first Multiply the 9s first
343 5 + 16 1213 - 729
21 484

Problem 2[edit]

2.a 10^4
2.b 10^7
2.c 10^10

Answers

2.a 10^4 = 10 \times 10 \times 10 \times 10 = 10,000
2.b 10^7 = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 = 10,000,000
2.c 10^10 = 10,000,000,000

Problem 3[edit]

Everybody is born to 2^1 biological parents. Our parents each had 2^1 + 2^1 biological parents. We can say that our grandparents are 2^2 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 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 256 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 2^5, scraps of paper left over. The general solution is:

 P = 2^r, 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 (2^8) 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.