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Transcript of Watch “Powers of 10” micro.magnet.fsu/primer/java/scienceopticsu/powersof10
Watch “Powers of 10”
http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/
Evaluating Exponents with Negative Bases
1. (–4)2
(–4)•(–4)
16
Since the negative sign is inside the parenthesis, keep it with the “4” when you multiply.
Since the negative sign is outside the parenthesis, leave it alone until the end.
Multiply 4•4...
Then, add the negative sign.3) –(3)3 4) (–3)3 5) –(2)5 6) (–2)5 7) –(1)7 8) (–7)1 –(3)•(3)•(3) (–3)•(–3)•(–3) –(2)•(2)•(2)•(2)•(2) (–2)•(–2)•(–2)•(–2)•(–2) –
(1)•(1)•(1)•(1)•(1)•(1)•(1) (–7)–(27) or –27 –27 –(32) or –32 –32 –(1) or –1 –7
2. – (4)2
–(4)•(4)
–( 16 )
–16ODD EXPONENTS
EVEN EXPONENTS
9) –(3)2 10) (–3)2 11) –(2)4 12) (–2)4 13) –(1)6 14) (–7)2
–(3)•(3) (–3)•(–3) –(2)•(2)•(2)•(2) (–2)•(–2)•(–2)•(–2) –(1)•(1)•(1)•(1)•(1)•(1) (–
7)•(–7) –(9)or –9 9 –(16) or –16 16 –(1) or –1
49
Evaluating Exponents to the Zero Power, x0
1. 40 Everything to the zero power is 1.
40 = 1
2. (–4)0 Since the negative sign is inside the parenthesis (–), take the whole thing, –4, to the zero power.
Everything, even negative integers, to the zero power is 1.
(–4)0 = 1
3. –(4)0
–(40)–(1)
4. –(3.6)0 5. (–7)0 6. 610 7 . –20 8. (–10)0
–(3.6)0 = –1
(–7)0 = 1 610 = 1 –(2)0 = –1 (–10)0 = 1
Since the negative sign is outside the parenthesis, leave the negative sign alone.
Only take 4 to the zero power.
At the end, add the negative sign.–1
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.= 24 There are 24
cells after the fourth cell division.
Understanding Exponents
2 • 2 • 2 • 2
The “2” is called the base.
The power of “4” is called the exponent.
Evaluating Exponents
Understanding Exponents
Evaluating Exponents
Writing Negative Exponents as Fractions
1. 6–3To evaluate a negative exponent, look at this pattern.
63
= 6•6•6 = 216
62
= 6•6 = 36
61
= 6 = 6What’s another way to get from 216 --> 36 ?Divide by
6.So, if you decrease the exponent by 1, divide by 6.
60
= 6 ÷ 6 = 1
6–1
= 1 ÷ 6 =
6–2
= ÷ =
6–3
= ÷ 6 =
÷ 6
61
61
361
Do you notice a shortcut for finding
the value of negative exponents?
If 62
= 36 .. and
6-2 = 1 .
36 ... then, what’s the value of...
361
216
116
Remember:
1. KEEP2. CHANGE 3. FLIP
If 63 = 216, ..
Evaluate each exponent term
Writing Negative Exponents as Fractions
Writing Negative Exponents as Decimals
there it is