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We say is in exponential notation and is in expanded notation.
For any expression is a factor multiplied by itself times if is a positive integer.
The expression is read to the power.
For powers of and we have special names.
[link] lists some examples of expressions written in exponential notation.
Exponential Notation | In Words |
---|---|
to the second power, or squared | |
to the third power, or cubed | |
to the fourth power | |
to the fifth power |
Write each expression in exponential form:
ⓐ The base 16 is a factor 7 times. | |
ⓑ The base 9 is a factor 5 times. | |
ⓒ The base is a factor 4 times. | |
ⓓ The base is a factor 8 times. |
Write each exponential expression in expanded form:
ⓐ The base is and the exponent is so means
ⓑ The base is and the exponent is so means
Write each exponential expression in expanded form:
Write each exponential expression in expanded form:
To simplify an exponential expression without using a calculator, we write it in expanded form and then multiply the factors.
Simplify:
Expand the expression. | |
Multiply left to right. | |
Multiply. |
We’ve introduced most of the symbols and notation used in algebra, but now we need to clarify the order of operations . Otherwise, expressions may have different meanings, and they may result in different values.
For example, consider the expression:
Imagine the confusion that could result if every problem had several different correct answers. The same expression should give the same result. So mathematicians established some guidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.
When simplifying mathematical expressions perform the operations in the following order:
1. P arentheses and other Grouping Symbols
2. E xponents
3. M ultiplication and D ivision
4. A ddition and S ubtraction
Students often ask, “How will I remember the order?” Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase. P lease E xcuse M y D ear A unt S ally.
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