Download Exponents

Exponents
32
base

take three, twice

3 to the second power

three squared
92=
3 3=
exponent
2 4=
6 1=
4•4•4•4•4 =
Any number to the first power equals that number
91=
121=
3331=
Any number to the zero power ALWAYS equals to 1
80=
990=
4210=
Any number to the second power is called ‘squared’
72=
9 2=
1 2=
First 10 squared numbers
12=
2 2=
3 2=
4 2=
5 2=
62=
7 2=
8 2=
9 2=
102=
Any number to the third power is called ‘cubed’
10100= googol
Order of Operations
Please ( )
Excuse exponent 2
My
*
Dear

Aunt
+
Sally
_
left to right
6
7 + 36  6 = 13
16 – 4  2
4+5*9
57  (42 + 3)
5 + 4 X 32
9  32 –1
Scientific or Algebraic calculator ALWAYS uses order of operations
Arithmetic calculator ALWAYS goes left to right
Divisibility
Divisor
Rule
2
any even number
3
the sum of the digits must be divisible by 3
5
the digit in the ones place must be 0 or 5
6
any number that is divisible by both 3 and 2
9
the sum of the digits must be divisible by 9
10
the digit in the ones place must be 0
Prime numbers- have exactly 2 factors, 1 and itself
Composite numbers – more than 2 factors
Prime factorization
Factor Trees – goals
1. to end up with all prime numbers
2. put prime numbers in order smallest to largest
3. can you use exponents
20 = 1, 20
2, 10
1, 2, 4, 5, 10, 20
4, 5
16 = 1, 16
4, 4
1, 42,16
Multiples – MULTIPLY – get LARGER
Multiply – get larger
think rabbits
Multiples of 6:
0x6=0
1x6=
2x6=
3x6=
4x6=
Factors – break down, get smaller
Now using prime factorization find the
Greatest Common Factor GCF
1. Get prime factorization
2. lowest power of common factors
HOW LOW CAN YOU GO?
Lowest Common Multiple LCM
Multiples of 8 are 8, 16, 24, 32, …
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, …
Multiples of 9 are 9, 18, …
Multiples of 6 are 6, 12, 18, …