1. Powers and Exponents, Square Roots
Pg. 25 – 28,

2. Definitions
FACTORS – Two or more numbers multiplied together to form a product
5 • 7 = 35
5 and 7 are the factors
35 is the product
When the same factor is used, you can use an exponent.
3 • 3 = 9, or
32 = 9
3 is the BASE and 2 is the EXPONENT

3. Powers Numbers expressed by using exponents are called POWERS.
53 is “ 5 to the third power or 5 cubed.
53 = 5 • 5 • 5
125
34 is “3 raised to the fourth power”
34 = 3 • 3 • 3 • 3 81
42 is “4 raised to the second power or 4 squared”
42 = 4 • 4 16

4. Write each power as a product of the same factor62
6 • 6 74
7 • 7 • 7 • 7 26
2 • 2 • 2 • 2 • 2 • 2

5. More Definitions
You can EVALUATE, or find the value of, powers by multiplying the factors.
Numbers written without exponents are in STANDARD FORM.
Evaluate 63
6 • 6 • 6
36 • 6
216
Numbers written with exponents are in EXPONENTIAL FORM.
9 • 9 • 9 •9 94

6. Squares and Square Roots
The product of a number and itself is the SQUARE of that number.
2 • 2 = 22 = 4
Numbers like 9, 25 and 81 are called PERFECT SQUARES.
32 = 9
52 = 25
92 = 81
The SQUARE ROOT of a number is one of its two equal factors
9 =3
25 =5
81 =9

7. Estimate square roots Estimate the 60
22 = 4, 32 = 9, 42 = 16, 52 = 25, 62 = 36, 72 = 49, 82 = 64, 92 = 81, 102 = 100
Estimate the 60
60 is not a perfect square. 60 lies between 49 (72) and 64 (82).
Since 60 is closest to 64, the best whole number estimate is 8
Estimate the 17
17 is not a perfect square. It lies between 16 (42) and 25 (52).
Since 17 is closest to 16, the best whole number estimate is 4.
Any number that is not a perfect square has a square root that is an IRRATIONAL NUMBER.