Suppose you have the expression:
How could you write this expression in a more concise way?
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James Sousa: Exponential Notation
Guidance
In the expression , the is called the base and the is called the exponent . Exponents are often referred to as powers . When an exponent is a positive whole number, it tells you how many times to multiply the base by itself. For example:
- .
There are many rules that have to do with exponents (often called the Laws of Exponents ) that are helpful to know so that you can work with expressions and equations that involve exponents more easily. Here you will learn two rules that have to do with exponents and products.
RULE: To multiply two terms with the same base, add the exponents.
RULE: To raise a product to a power, raise each of the factors to the power.
Example A
Simplify .
Solution:
The answer can be taken one step further. The base is numerical so the term can be evaluated.
Example B
Simplify .
Solution:
Example C
Simplify .
Solution:
Example D
Simplify .
Solution:
Concept Problem Revisited
can be rewritten as . Then, you can use the rules of exponents to simplify the expression to . This is certainly much quicker to write!
Guided Practice
Simplify each of the following expressions.
1.
2.
3.
Answers:
1. . Here are the steps:
2. . Here are the steps:
3. . Here are the steps:
OR
Explore More
Simplify each of the following expressions, if possible.
Expand and then simplify each of the following expressions.
- Hint: Look for a pattern in the previous two problems.