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2.3 Exponents and Powers
I can read powers and express numbers using exponents
Vocabulary
Exponent:
the small number written above and to the right of a
number called the base. It tells how many times to
multiply the base by itself.
exponent

Example: 25 = 2 x 2 x 2 x 2 x 2 = 32


base
2 multiplied by
itself five times
25 is read “two to the fifth power”
Powers: numbers expressed using exponents
Squared:
a number multiplied by itself two times; a number to
the power of two.
Example: 4 squared is 42 = 4 x 4 = 16
Cubed:
A number multiplied by itself three times; a number to
the power of three.
Example: 4 cubed is 43 = 4 x 4 x 4 = 64
Value:
How much the expression is worth once multiplied out
Notes:
10 is a special case. 10 raised to any power is simply the number
1 with the same number of zeros as the exponent.
Examples: 103 = 1 with 3 zeros = 1,000
108 = 1 with 8 zeros = 100,000,000
Applications
1) Write the product using exponents:
a. 3 x 3 x 3 x 3 x 3 = ____________
b. 20 x 20 x 20 x 20 x 20 x 20 x 20 x 20 = ___________
2) Write each power as the product of the same factor. Then
find the value.
a. 73 = ______ = 7 x 7 x 7 = 49 x 7 = 343
b. 105 = __________________________________
3) Write the prime factorization using exponents:
a. 36
36
6
3 2
b.
96
6
3 2
36 = 2 x 2 x 3 x 3 = 22 x 32
2.3 Exponents and Powers