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Definition
When a number is repeatedly multiplied by itself, we get the powers of that number. Thus, a· a is called the second power of a, or "a squared." a· a· a is the third power of a, or "a cubed." aaaa is a to the fourth power, and so on. The first power of a is a itself.
Now, rather than write aaaa, we write a just once and place a small number 4: a4 ( "a to the 4th"). That small 4 is called an exponent. It indicates the number of times to repeat a as a factor.
83 ("8 to the third") means 8· 8· 8.
Problem 3. Read, then calculate each of the following.
a) 5² "5 to the second power" or "5 squared" = 25.
b) 23 "2 to the third power" or "2 cubed" = 8.
c) 104 "10 to the fourth" = 10,000.
d) 121 "12 to the first" = 12. |
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Term
| Define the order of operations |
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Definition
The order of operations is as follows:
(1) Evaluate the parentheses, if there are any, and if they require evaluation.
(2) Evaluate the powers, that is, the exponents.
(3) Multiply or divide -- it does not matter.
(4) Add or subtract. |
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Term
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Definition
Terms versus factors.
When numbers are added or subtracted, they are called terms.
When numbers are multiplied, they are called factors.
Here is a sum of four terms: a − b + c − d.
In algebra we speak of a "sum" of several terms, even though there are subtractions. In other words, anything that looks like what you see above, we call a sum.
Here is a product of four factors: abcd.
The word factors always signifies multiplication.
And again, we speak of the "product" abcd, even though we do not name an answer.
Problem 2. In the following expression, how many terms are there? And each term has how many factors?
2a + 4ab + 5a(b + c)
There are three terms. 2a is the first term. It has two factors: 2 and a.
4ab is the second term. It has three factors: 4, a, and b.
And 5a(b + c) is all one term. It also has three factors: 5, a, and (b + c). The parentheses mean that we should treat whatever is enclosed as one number. |
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Term
Question 5. What do we mean by the value of a letter?
The value of a letter is a number. It is the number that will replace the letter when we do the order of operations. |
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Definition
Question 6. What does it mean to evaluate an expression?
It means to replace each letter with its value, and then do the order of operations. |
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Definition
Question 6. What does it mean to evaluate an expression?
It means to replace each letter with its value, and then do the order of operations. |
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