GRE - Powers Refresher
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GRE
Powers Refresher
base Æ 25 |
Å exponent |
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= 2 ×2 ×2 ×2 ×2 |
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Examples: |
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52 |
34 |
106 |
= 5 ×5 |
= 3 ×3 ×3 ×3 |
= 10 ×10 ×10 ×10 ×10 ×10 |
= 25 |
= 81 |
= 1,000,000 |
Practice: Evaluate the following |
Answers: |
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a) 3 3 = |
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a) 3 3 = 27 |
b) 2 4 = |
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b) 2 4 = 16 |
c) 10 5 = |
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c) 10 5 = 100,000 |
d) (-2) 6 = |
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d) (-2) 6 = 64 |
e) 5 3 = |
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e) 5 3 = 125 |
f) 7 1 = |
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f) 7 1 = 7 |
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Practice: Find the value of x |
Answers: |
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a) 4 x = 64 |
a) 4 3 = 64 |
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b) x 3 = 8 |
b) 2 3 = 8 |
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c) 10 x = 10,000 |
c) 10 4 = 10,000 |
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d) x 3 = 27 |
d) 3 3 = 27 |
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e) 13 x = 13 |
e) 13 1 = 13 |
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f) x 2 = 1,000,000 |
f) 1000 2 = 1,000,000 |
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GRE
Powers Refresher
Product Law
xa xb = xa+b
Examples:
85 87 = 812
(−3)10 (−3)9 = (−3)19
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4 6 |
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4 4 |
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4 10 |
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7 |
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7 |
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= |
7 |
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Practice: Simplify the following
a) 64 63 62 6 =
(−5)21
b)(−5)3 =
c)2 8 2 2 10 =
3 3 3
d)(54 )11 =
Quotient Law
xa ÷ xb = |
xa |
= xa−b |
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xb |
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Examples:
49 ÷ 46 = 43
511 = 57
54
(−2.8)30 = (−2.8)20 (−2.8)10
e)85 84 83 =
86
f)(23 )4 5 =
g)7 7 7 7 7 7 7 7 7 =
h)x5 x4 x13 =
x6
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i) |
x (x5 )2 x7 |
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(x4 )3 |
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Power Law
(xa )b = xab
Examples:
(113 )5 = 1115
(−3.9)2 10 = (−3.9)20
(843 )7 = 8421
Answers:
a)610
b)(−5)18
2 19
c)3
d)544
e)86
f)260
g)79
h)x16
i)x6
2
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Powers Refresher |
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GRE |
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Negative Powers
x −n = x1n
Examples:
3−4 = 314 = 811
10−2 = 1012 = 1001 7−1 = 711 = 71
Practice: Evaluate the following
a)5 -2 =
b)2 -5 =
c)10 -4 =
d)(-3) -1 =
e)4 -3 =
f)11 -1 =
Practice: Find the value of x a) 2x = 1281
b) |
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−3 |
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1 |
x |
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= 1,000,000 |
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c)5x = 6251
d)x−2 = 2549
e)x−83 = 1
Answers:
a) 5 -2 = 251
1 b) 2 -5 = 32
c) 10 -4 = |
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1 |
10,000 |
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d) (-3) -1 = − |
1 |
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3 |
e) 4 -3 = |
1 |
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64 |
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f) 11 -1 = |
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1 |
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11 |
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Answers:
a)2−7 = 1281
b) |
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−3 |
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1 |
100 |
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= 1,000,000 |
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c)5−4 = 6251
d)5 −2 = 49
7 25
e) 1−83 = 1
3