# Algebra/Arithmetic/Exponent Problems

## Problem 1

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

## 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?