Laws of Exponents
If:
Example:
Another Example For Negative Exponents
Still More Examples
Why?
More Exponents
Example:
More Exponents
Example:
Example:
If a and b are not zero,
Example:
Example:
Note that 
So we have just " factored " 1,000
Example:
If 
Example:
Example:
Practice
Simplify each expression (you may leave
answers in exponential form .)
Answers to Practice Problems
( 
Definitions
• Square Root - a number that when multiplied by
itself produces a given number.
Example:
3 is a square root of 9.
-3 is also a
• Radical Sign 
The
symbol for the positive
square root. square root of 9.
By convention, the radical sign,
a designates
only the positive square root.
Radical Sign 
Radicand
Squaring and Taking a Square Root
are Inverse Operations
Like Addition is to Subtraction
Like Multiplication is to Division
Square Numbers and Square Roots
Perspective
When taking a Square Root, one question you
could ask yourself is:
"What number times itself is the radicand?”
"What number times itself is 36?"
Practice Taking the Square Root
Answers to Practice
Question
Between which whole numbers is the
Square Root of 45?
45 is not a square number, but it is
between two square numbers.
36 < 45 < 49
and
and
is a little less than
7.
Practice
Estimate the value of
Practice
Estimate the value of
Since 64 < 67 < 81
and
and
is a little more than
8.
Check Your Understanding
Fill in the missing parts
Check your Understanding
Part 2
1. Explain how 9 and 81 are related.
___________________________
___________________________
2. Without a calculator , identify the two integers
between which the square root lies, and explain
why.
Opening Activity
Your rich uncle needs your help in his office for a 30
day month. He made an unusual offer to pay you 1¢
the first day, 2¢ the second day, 4¢ the third day,
each day doubling the previous days pay. Of course,
you were insulted and were about to refuse
employment for the month when he said, "Ok, ok, I
really need your help. So how about $1,000.00 a
day with $1,000.00 raise each day." You gladly
accepted and your rich eccentric uncle laughed all
the way back to his office. What did you do that
was so funny to him?
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