Transcript exponent

Exponents
• Two or more numbers that are multiplied
together to form a product are called factors.
• When the same factor is used, you may use
an exponent to simplify the notation.
The dots
indicate
multiplication.
The exponent tells
how many times the
base is repeated.
16 = 2 2 2 2 =
Common
factors
The base is the
common factor.
4
2
• Numbers expressed using exponents
are called powers.
Powers
Words
2
5
Five to the second power OR
Five squared
3
4
Four to the third power OR
Four cubed
4
2
Two to the fourth power
Write each power as a product of the
same factor.
142
14 × 14
54
5 5 5 5
75
7×7×7×7×7
Write each product in exponential form.
11 11 11
11³
3 × 3 × 3 × 3 × 3 ×3
36
15 15 8 8
15² 8²
7×7×7×3×3
73 × 32
Evaluate each expression. Find the
standard form.
3 squared
32
3×3
9
42 × 33
4×4×3×3×3
16 × 27
432
Evaluate each expression. Find the standard
form.
ten to the fifth power
105
10 10 10 10 10
100,000
three to the fourth power
34
3×3×3×3
9 × 9
81
Exponent
Form
Factor
Form
Standard
Form
25
2x2x2x2x2
32
72
7x7
49
43
4x4x4
64
104
10 x 10 x 10 x 10
10,000
53
5x5x5
125
Exponents tell how many times a number, called a
BASE, is used as a factor.
6² = 6 x 6
In 6 x 6, 6 is used as a factor twice. When you compute
6 x 6 or 6², you are finding the SQUARE of 6.
6
6
Find the squares of the following
numbers:
1) 8 =
2
2
2) 12 =
3)
2
9 =
2
4) 10 =
64
144
81
100
(8x8)
( 12 x 12 )
(9x9)
( 10 x 10 )
Numbers like 36, 49, and 625 are
called PERFECT SQUARES, because
they are the squares of whole
numbers.
6
6
6² = 36
If 6 is the number you would square to
find 36, then 6 is the square root of 36.
√36 = 6
What number would you square or is
the square root of 9?
3
9
3
A radical sign ( √ ) is placed over a
number when the square root is requested.
What number would you square or is
the square root of the following
numbers:
1) √ 81 =
9
2) √ 121 = 11
(9x9)
( 11 x 11 )
3) √ 49 = 7
(7x7)
4) √ 196 =14
( 14 x 14 )
When given multiple choice answers to
choose from for squares and square roots,
first state the answer to the question, then
match your answer with a multiple choice
answer that represents the same.
1) Which of the following best represents √ 81 ?
81
81
9
18
9
2
9
9
2) Which if the following represents 3² ?
2
6
5
6 3
15
3
9
9
9
Which of the following best represents
6
√36 ?
1)
216
2)
12
3)
6
4)
36
6
6
6
Which of the following best represents
16
4² ?
6
16
1)
2)
3)
4)
4 16
4
4
Construct a Square Root Chart with
your partner showing the numbers
that 1-15 are the square roots of!
Example
√1
Square
Root
1
√4
2
√9
3
√ 16
4
√ 25
5
YOUR ASSIGNMENT
• Square and Square Roots WS
YOUR ASSIGNMENT ---• Pg 32 #12-32 evens,
• Pg 36 #10-30 evens