Numbers and Quantities
The rules of powers are shown below. It’s important that you learn these. We’ll take a closer look at the rules and see how they’re used.
Rule
Rules for Powers
Remember that the letters and can be any number or letter. These rules are valid when calculating with both numbers and letters.
Let’s have a look at some examples where we use the rules for powers.
Rule 1
First, I will show you how to use Rule .
Rule
Example 1
Let’s see why this rule is valid:
This gives us that
Rule 2
Next, we will look at Rule .
Rule
Example 2
Let’s see why this rule is valid:
This means that
Rule 3
Now you will see how to use Rule .
Rule
Example 3
Let’s see why this rule is valid:
That gives us
Rule 4
Here you will see how to use Rule .
Rule
Example 4
Let’s see why this rule is valid:
This means that
Rule 5
Now, we will take a look at Rule .
Rule
Example 5
Let’s see why this rule is valid:
showing us that
Rule 6
Now you will see how to use Rule .
Rule
Example 6
Let’s see why this rule is valid:
showing that
Rule 7
Now, let’s look at Rule .
Rule
Example 7
Let’s see why this rule is valid. Here we need to be a bit more thorough. We know that . With this as a starting point, we get
Rule 8
Finally, I will show you how to use Rule .
Rule
Example 8
Let’s see why this rule is valid. Here we will use a trick, namely that . It might seem a bit funny, but as long as it works, which it does, we can use it to help us out.
This shows us that
Combined examples
Here are some examples that require you to use several rules at once.
Example 9
Example 10
