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# Powers and Exponents

Powers and Exponents Review for Algebra 1
by

## Rob Frederick

on 22 August 2013

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#### Transcript of Powers and Exponents

Powers and Exponents
A "power" is an expression written with an "exponent" and a "base" or the value of such an expression:
Power!
3
2
The , 3,
is the number
that is used
as the factor.
base
The ,
2, tells how many
times the base is
used as a factor.
exponent
Bell Ringer:
Bonus:
1.) (-2)(-2)(-2)
2.) (5/7)(5/7)
3.) |-40|/|8|
Evaluate each expression:
14cdf
_
8ce
Words
Multiplication
Power
Value
3 to the first 3 3 3

3 to the second 3 x 3 3 9

3 to the third 3 x 3 x 3 3 27

3 to the fourth 3 x 3 x 3 x 3 3 81

3 to the fifth 3 x 3 x 3 x 3 x 3 3 243
1

2

3

4

5
Evaluating Powers:
(-2)
3
-5
2
(2/3)
2
Writing Powers:
Write each number as a power of the given base:
8; base 2
8 = (2)(2)(2)
= 2
3
-125; base 5
-125 = (5)(5)(5)

= 5
3
Application:
A certain bacteria doubles every hour.
There is 1 bacterium on a slide.
If each bacterium splits (and therefore
doubles) once per hour, how many bacteria
will be on the slide after 6 hours?
Application:
We can make a diagram to "see" what's
happening each hour
Application:
After 1 hour: 2
After 3 hours: 8
After 2 hours: 4
Application:
Notice that after each hour, the number
of bacteria is a power of 2:
1 hour: 2 or 2 bacteria
2 hours: 4 or 2 bacteria
3 hours: 8 or 2 bacteria

So, after 6 hours there will be 2 bacteria
or 64 bacteria.
1
6
2
3

(-2)(-2)(-2) = -8
-1(5)(5) = -25
(2/3)(2/3) = 4/9
Full transcript