Algebra/Arithmetic/Exponent Problems

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Problem 1

$7^{3}$
$5+4^{2}$
$1213-9^{3}$

Problem 2

Examples

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

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

Problem 3

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

Example

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

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

Problem 5

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

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