What happens when a term involving exponents is raised to a power? For example take an expression like 
. You are probably aware that exponent is another way of representing the repeated multiplication of the same term by itself. In our example:
. You are probably aware that exponent is another way of representing the repeated multiplication of the same term by itself. In our example:
You can simplify the above expression using the exponent multiplication rule. For example:
The above example illustrates that whenever an exponent is raised to a power, you can multiply the exponent and the power. In the above example:
When a number with an exponent is raised to a power, you can simplify the expression by multiplying the exponent and the power.
Note: If the number inside the bracket is an expression involving addition or subtraction, you cannot use this rule.
For Example:
Exponents or raising a number to a power does not distribute like a multiplication operation.
These are simple concepts. Let’s look at some examples of how they are used:
Example:
Which of the following expressions is equivalent to 
?
?
A) 
B) 
C) 
D) 
E) 
Solution:
You can solve this question using your calculator. However it can be solved very easily using simple application of exponent rules.
One of the first things you can notice is that the number 
can be expressed as 
. This way both numbers can have the same base.
can be expressed as . This way both numbers can have the same base.
Step 1: We can write 
Step 2: By substituting the value of 
in the expression, the problem is reduced to a simple exponent multiplication problem:
in the expression, the problem is reduced to a simple exponent multiplication problem:
C is the correct answer.
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