Watch “Powers of 10”
http://micro.magnet.fsu.edu/primer/java/scienceopti
csu/powersof10/
Evaluating Exponents with Negative Bases
(–4)2
1.
Since the negative sign is inside the
parenthesis, keep it with the “4” when you
multiply.
(–4)•(–4)
16
Since the negative sign is outside the
parenthesis, leave it alone until the end.
– (4)2
2.
–(4)•(4)
–( 16 )
Multiply 4•4...
–16
Then, add the negative sign.
ODD EXPONENTS
3)
–(3)3
–(3)•(3)•(3)
–(27) or –27
4) (–3)3
(–3)•(–3)•(–3)
–27
5)
–(2)5
6) (–2)5
–(2)•(2)•(2)•(2)•(2) (–2)•(–2)•(–2)•(–2)•(–2)
–32
–(32) or –32
7)
–(1)7
–(1)•(1)•(1)•(1)•(1)•(1)•(1)
–(1) or –1
8) (–7)1
(–7)
–7
EVEN EXPONENTS
9) –(3)
2
–(3)•(3)
–(9)or –9
10) (–3)
2
(–3)•(–3)
9
11) –(2)
4
–(2)•(2)•(2)•(2)
–(16) or –16
12) (–2)
4
(–2)•(–2)•(–2)•(–2)
16
13) –(1)
6
–(1)•(1)•(1)•(1)•(1)•(1)
–(1) or –1
14) (–7)
2
(–7)•(–7)
49
0
Evaluating Exponents to the Zero Power, x
40
40
1.
Everything to the zero power is 1.
=1
Since the negative sign is inside the parenthesis (–), take
the whole thing, –4, to the zero power.
0
2.
(–4)
(–4)0
=1
–(4)0
3.
–
Since the negative sign is outside the parenthesis, leave the
negative sign alone.
(40)
Only take 4 to the zero power.
–(1)
At the end, add the negative sign.
–1
4.
–(3.6)0
–(3.6)0
= –1
Everything, even negative integers, to the zero power is 1.
5.
(–7)0
(–7)0 = 1
6.
610
610 = 1
7 . – 20
–(2)0
8.
(–10)0
= –1 (–10)0 = 1
Understanding Exponents
A plant grows when its cells divide into pairs, as shown below. What is
another way to write the number of cells after the fourth division?
After the fourth cell division described above, there are 2 • 2 • 2 • 2 cells.
4 The power of “4” is called the exponent.
There are 24
2• 2•2•2= 2
cells after the
The “2” is called the base.
fourth cell
division.
Evaluating Exponents
Understanding Exponents
Evaluating Exponents
Writing Negative Exponents as Fractions
1. 6
–3
To evaluate a negative exponent, look at this pattern.
3
6
6
6
2
1
=
6•6•6
= 216 ÷ 6
=
6•6
= 36
=
6
=6
What’s another way to get from 216 --> 36 ? Divide by 6.
So, if you decrease the exponent by 1, divide by 6.
Do you notice a shortcut
for finding the value of
negative exponents?
If
2
6 = 36 ..
-2
and
6 =
If
3
1
36
6 = 216, ..
.
6
6
6
0
–1
–2
=
6÷6
= 1
=
1÷6
=
1 6
6÷ 1
1
= 6
1
= 36
... then, what’s the value of...
6
–3
=
1
÷6
36
Remember:
1. KEEP
2. CHANGE
3. FLIP
=
1
216
Writing Negative Exponents as Fractions
Evaluate each exponent term
Writing Negative Exponents as Decimals
there it is