powers and exponents. objective you will be able to write repeated multiplication using exponents....
TRANSCRIPT
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.