# Algebra/Arithmetic/Exponent Problems

1

 $7^{3}=$ 2

 $5+4^{2}=$ 3

 $1,213-9^{3}=$ 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.

4

 $10^{4}=$ 5

 $10^{7}=$ 6

 $10^{10}=$ 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:

7 How many times would 2 be multiplied to determine the number of great grandparents?

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

9 How many people would be our 28 ancestors?

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.

10 Identify the square numbers between 50 and 100 inclusive.

 , and

11 Identify the square numbers between 160 and 200.

 and

12 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?