# Algebra/Arithmetic/Exponent Problems

1

 ${\displaystyle 7^{3}=}$

2

 ${\displaystyle 5+4^{2}=}$

3

 ${\displaystyle 1,213-9^{3}=}$
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, ${\displaystyle 10^{1}=10}$, that is, 10 to the first power has one zero after the 1.

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

4

 ${\displaystyle 10^{4}=}$

5

 ${\displaystyle 10^{7}=}$

6

 ${\displaystyle 10^{10}=}$
Everybody is born to ${\displaystyle 2^{1}}$ biological parents. Our parents each had ${\displaystyle 2^{1}+2^{1}}$ biological parents. We can say that our grandparents are ${\displaystyle 2^{2}}$ 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
${\displaystyle 4^{2}=16}$ is too small
${\displaystyle 5^{2}=25}$ is in the range
${\displaystyle 6^{2}=36}$ is in the range
${\displaystyle 7^{2}=49}$ 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?