Powers and Exponents. Objective You will be able to write repeated multiplication using exponents. Word Watch: -power -base -exponent.
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Powers and Exponents
Objective
You will be able to write repeated multiplication using exponents.
Word Watch: -power-base-exponent
Vocab
A power is a way of writing repeated multiplication.
The base of a power is the factor.
The exponent of a power is the number of times the factor is used.
4 6 exponentBase
(power
= 4 x 4 x 4 x 4 x 4 x 446
4 is a factor 6 times
The power is read “four to the sixth power.”
Algebra…
an= a x a x a x… x a
a is a factor n times
Writing powers
2 x 2 x 2 x 2 = 24
2 is a factor 4 times
This is read “two to the fourth power.”
Example
6 x 6 x 6 = ??
6 x 6 x 6 = 63
This is read, “six cubed.”
YOUR TURN
5 x 5 x 5 x 5 x 5 = ??
5 x 5 x 5 x 5 x 5 = 55
How is this read??
“five to the fifth power”
GO THE OTHER WAY!!
Write each expanded form in exponent form.
1) 4 x 4 x 4 x 444
2) (-8)(-8)(-8)
(-8)3
Another example:
1) pppqqqq
=p3q4
HOWEVER,you always want the bigger exponents first…. q4p3
2) ffttffrr
=f4t2r2
Evaluate the power (write in standard form)
72 == 49
43 == 64
31 == 3
4 x 4 x 4
7 x 7
3
YOUR TURN
Write the power in words, then solve:
26 Two to the sixth power = 2 x 2 x 2 x 2 x 2 x 2 = 64
62 Six squared = 6 x 6 = 36
Evaluating Powers with Variables
Evaluate x2 when x = 9X2 = 92Substitute 9 for x
= 9 x 9
= 81
Another example…
Evaluate b3 when b = 7b3 = 73
= 7 x 7 x 7
= 343
YOUR TURN!!
Evaluate m8 when m = 2m8 = 28
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2= 256
Another one…
Evaluate p3 when p = 10
p3 = 103
= 10 x 10 x 10
= 1000
ZERO POWER
Anything to the 0 power = 1!!
ThOuGht Of ThE dAy
• Butterflies taste with their feet.
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