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| Exponentiation
- Powers or Indices |
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| Exponentiation
- Powers or Indices |
Integral exponentiation - integer exponents
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Square or the second power
(potency)
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The square of a product and quotient
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| Integral exponentiation - integer exponents
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| Exponentiation,
powers, exponents (indices) |
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Rules |
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Examples |
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| 1) |
a
· a
· ... · a
=
an,
a
Î Q,
n Î N
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a3
= a
· a
· a,
24 =
2 ·
2 ·
2 ·
2
= 16, |
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n
factors, a
-base, n
-exponent (index) |
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(-1) · (-1)
· (-1)
· (-1) =
(-1)4
= 1, |
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| 2) |
a
= a1,
or a1
=
a, |
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2 = 21,
(-3)1
= -3, |
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| 3) |
a0
= 1,
an ¸
an
= 1, |
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23
¸ 23
= 23 -
3 =
20
= 1,
(ab3)0
= 1, |
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| 4) |
1n
=
1, |
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15
= 1,
(-1)5
= -1, |
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| 5) |
(-
a)2n
= a2n,
2n
-even exponents |
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(-
5)4 = 54
= 625 |
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| 6) |
(-
a)2n
-1
= - a2n
-1,
2n-1
-odd exponents |
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(-
2)3 = -
23 =
- 8 |
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| 7) |
(-1)2n
= 1, |
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(-1)6
= 1, |
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| 8( |
(-1)2n
-1
= -1, |
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(-1)7
= -1. |
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| Square or the second power
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| 1) |
a2
=
a
· a,
12
= 1 · 1 = 1, |
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52 =
5 ·
5 = 25,
0.42 =
0.4 ·
0.4 = 0.16, |
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| 2) |
(-
r)2 =
(- r)
· (-
r)
=
r2, |
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(-
4)2 = (-
4)
· (-
4) = 16,
(-1)2 = 12
= 1. |
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| Square of a product and quotient |
| 1) |
(a
· b)2
=
a2
· b2, |
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(3 ·
6)2 = 32 ·
62 = 9 ·
36 = 324, |
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| 2) |
a2
· b2
· c2
=
(a · b
· c)2, |
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0.12
· 1.22
· 102 =
(0.1 ·
1.2 ·
10)2 = 1.22, |
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| 3) |
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| 4) |
(a
¸
b)2
=
a2
¸
b2, |
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(6
¸
2)2 =
62
¸
22 = 36
¸
4 = 9, |
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| 5) |
a2
¸
b2
= (a
¸
b)2, |
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642
¸
(-
16)2 =
[64
¸
(-
16)]2 = (-
4)2 = 16. |
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| Beginning
Algebra Contents B |
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| Copyright
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