Download Exponents Exploration - 09-10

Exponents Exploration
Prove your own properties!
Name: ________________________ Period: ____
2x
Power
25
3x
Answer
Power
35
4x
Answer
Power
45
24
34
44
23
33
43
22
32
42
21
31
41
Answer
Look at the tables above. Describe the patterns that you see:
 What happens to the BASE each time?

What happens to the EXPONENT each time?

What happens to the ANSWER each time?
Write your own “conjecture” about any number n raised to the 1st power. In other words, what
is any number to the first power?
Test your conjecture: Find 51 = _____ 161 = ______ (-3)1 = ____
Look at the 2x table. If you divide each answer by 2 (the base), you get the next answer. Well,
if that is the case, what do you think will happen if you extend the table to 2 raised to the ZERO
POWER? 20 = _______.
Check your answer on your calculator. Were you correct? _______
Utilizing the pattern that you found above, continue the tables below:
Power
20
Answer
Power
30
Answer
Power
40
Answer
Will this work for any base? _______ Try it! Use your calculator to raise different numbers to
the zero power. Make sure you try 00.
Write a “conjecture” for raising a number to the ZERO POWER:
In the next set of tables, you are going to continue to use the same patterns as you did above
(divide each answer by the base). LEAVE YOUR ANSWERS AS FRACTIONS! (Some are done for
you)
2x
3x
4x
Power
Answer
Power
0
Answer
Power
2
1
3
4
2-1
1
2
3-1
4-1
2-2
3-2
4-2
2-3
3-3
4-3
2-4
3-4
0
4-4
1
81
Compare these tables to the first set of tables. What do you notice?
Write a “conjecture” for raising a number to a NEGATIVE POWER:
Properties of exponents: Expand first.
Then, re-write as a new power:
1)
x5
= x? =
x8
6)
34  35
Property: a-n =
2)
x8  x5
Property: am  an =
8
3)
4)
3
32
Property:
5)
7)
(32)4
8)
(x4)6
Property: (am)n =
x12
x7
9)
am
=
an
Property: a0 =
(2x2y)4
Property: (a  b)n =
x5
= x? =
5
x
10)
, a
Answer
0
 5x 3 
 4 
 y 
2
n
 a
Property:   =
b
1
16