Download Why Any Number to the Zero Power is Equal to One

Notes: Exponents and Square Roots Name___________KEY_______________Per___Date __________
Exponents
Fill in the blanks with the names. Use your past notes to help you.
43
Exponent – tells how many times the ____________________ is used as a factor (multiplied.)
Power – a number that can be expressed using an __________________________.
Write using exponents:
1)
8 . 8 . 8 . 8 . 8 .=
2) 10 . 10 . 10 . 10 . 10 . 10 . 10 . 10 =
Write as a product of repeated factors. Then simplify.
34 = 3 . 3 . 3 . 3 = _____
104 = 10 . 10 . 10 . 10 = _____
33 = _________ = _____
103 = ____________ = _____
32 = _________ = _____
102 = ____________ = _____
31 = _________ = _____
101 = ____________ = _____
30 = _____
100 = _____
Look at the patter to find the zero powers!!!
I. Square Roots and Irrational Numbers
Vocabulary:
Perfect Square – a number that is the second power (square) of an integer.
Examples: 32= 9 so 9 is a perfect square.
Square Root – a number that when multiplied by itself (when it is squared) forms a product that is a
perfect square.
The symbol
(a radical) means: “what number times itself (squared) gives you the number
under the radical symbol?”
1. Calculate the following:
25 =
9 =
16 =
12
12 is called an irrational number.
Irrational number - a decimal number that neither terminates, nor repeats.
Rational number – can be written as a ratio (fraction) and as a decimal it
terminates or repeats.
Tell if these numbers are rational or irrational and why.
14
100
-0.98
0.323223222322223……
0.232323232323….
π
Why is any Number to the Zero Power Equal to 1?
Fill in the table.
2 0= 1
2 1=
2 2=
2 3=
2 4=
2 5=
2 6=
2 7=
2 8=
2 0=
2 4=
2 3=
2 2=
2 1=
2 0=
What is an easy way to find the next factor?
Now fill in the table using the information above.
2 9=
2 8=
2 7=
2 6=
2 5=
As you move to the right in the table what is the pattern?_____________________________________
When you get to 21 what will you do to that product to move to 20?___________________________
What about the pattern for :
34 =
, 33 =
, 32 =
, 31 =
, 30 =
44 =
, 43 =
, 42 =
, 41 =
, 40 =
54 =
, 53 =
, 52 =
, 51 =
, 50 =
104 =
, 103 =
, 102 =
, 101 =
, 100 =
Should this pattern work for any number to the zero power?__________________________________
Notes: Exponents and Square Roots Name_______________________________Per___Date __________
Exponents
Fill in the blanks with the names. Use your past notes to help you.
43
Exponent – tells how many times the ____________________ is used as a factor (multiplied.)
Power – a number that can be expressed using an __________________________.
Write using exponents:
2)
8 . 8 . 8 . 8 . 8 .=
2) 10 . 10 . 10 . 10 . 10 . 10 . 10 . 10 =
Write as a product of repeated factors. Then simplify.
34 = 3 . 3 . 3 . 3 = _____
104 = 10 . 10 . 10 . 10 = _____
33 = _________ = _____
103 = ____________ = _____
32 = _________ = _____
102 = ____________ = _____
31 = _________ = _____
101 = ____________ = _____
30 = _____
100 = _____
Look at the patter to find the zero powers!!!
II. Square Roots and Irrational Numbers
Vocabulary:
Perfect Square – a number that is the _____________________ power (square) of an integer.
Examples: 32= 9 so 9 is a ________________________ square.
Square Root – a number that when multiplied by itself (when it is ________________________) forms a
product that is a perfect square.
The symbol
(a ____________________) means: “what number times itself (squared)
gives you the number under the radical symbol?”
2. Calculate the following:
25 =
9 =
16 =
12
12 is called an irrational number.
Irrational number - a decimal number that neither ______________________,
nor repeats.
Rational number – can be written as a __________________ (fraction) and as
a decimal it terminates or repeats.
Tell if these numbers are rational or irrational and why.
14
100
-0.98
0.323223222322223……
0.232323232323….
π
Why is any Number to the Zero Power Equal to 1?
Fill in the table.
2 0= 1
2 1=
2 2=
2 3=
2 4=
2 5=
2 6=
2 7=
2 8=
2 0=
2 4=
2 3=
2 2=
2 1=
2 0=
What is an easy way to find the next factor?
Now fill in the table using the information above.
2 9=
2 8=
2 7=
2 6=
2 5=
As you move to the right in the table what is the pattern?_____________________________________
When you get to 21 what will you do to that product to move to 20?___________________________
What about the pattern for :
34 =
, 33 =
, 32 =
, 31 =
, 30 =
44 =
, 43 =
, 42 =
, 41 =
, 40 =
54 =
, 53 =
, 52 =
, 51 =
, 50 =
104 =
, 103 =
, 102 =
, 101 =
, 100 =
Should this pattern work for any number to the zero power?__________________________________
Practice using EXPONENTS
Name_______________________________
Period________
Date __________________
Write using exponents.
1. 3 . 3 . 3 . 3. 3 = _____
2. 2.7 . 2.7 . 2.7 = _____
3. 11.6 . 11.6 . 11.6 . 11.6 = _____
4. 2 . 2 . 2 . 2 . 2 . 2 = _____
5. 4 . 4 . 4 . 4 . 4 . 4 . 4 . 4 = _____
Write as the product of repeated factors. Then simplify.
6.
24 = ______________________________________ = _________
7. 53 = ______________________________________ = _________
8. (0.5)3 = ______________________________________ = _________
9. 105 = ______________________________________ = _________
10. Fill in the blanks with <, >, or =. Show what each is equal to in order to verify your answer.
9 = 3 . 3 = 32 < 23
42
24
52
25
62
26
43
34
53
35
72
27
=2. 2.2=8
11. What do you notice usually happens as the exponent gets bigger and the base is smaller?
__________________________________________________________________________