# Algebra/Arithmetic/Exponent Problems

## Problem 1

1. ${\displaystyle 7^{3}}$
2. ${\displaystyle 5+4^{2}}$
3. ${\displaystyle 1213-9^{3}}$

## 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, ${\displaystyle 10^{1}=10}$, 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.

#### Problems

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

## Problem 3

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:
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
${\displaystyle 4^{2}=16}$ 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.

#### 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?