Algebra/Arithmetic/Exponent Problems

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Return to Exponents Arithmetic Exponent Problems Return to Roots


Problem 1[edit]

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

Problem 2[edit]

Examples[edit]

Calculating powers of 10 become easier when understanding that the exponent gives a clue to how many zeros there are after the 1.

For example, 10^1 = 10, that is, 10 to the first power has one zero after the 1.

10^2 = 100, or 10 \times 10 = 100 that is, 10 to the second power has two zeros after the 1.

Problems[edit]

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

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?

Problem 4[edit]

Example[edit]

We can identify the square numbers between two numbers by simply squaring basic numbers. For example:
To identify the square numbers between 20 and 40 we can say
4^2 = 16 is too small
5^2 = 25 is in the range
6^2 = 36 is in the range
7^2 - 49 is too large
So the square numbers in that range are 5 and 6.

Problems[edit]

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

Problem 5[edit]

You tear a piece of paper in half. Then, you tear each remaining sheet of paper in half again. You tear the collection of papers 5 times over all. When you are done, how many scraps of paper do you have?

Answers