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Laws of Exponents

Addition 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


( bases are different )

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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