GRE - Powers Refresher

GRE

Powers Refresher

base Æ 25	Å exponent
	= 2 ×2 ×2 ×2 ×2
Examples:
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:
a) 3 3 =		a) 3 3 = 27
b) 2 4 =		b) 2 4 = 16
c) 10 5 =		c) 10 5 = 100,000
d) (-2) 6 =		d) (-2) 6 = 64
e) 5 3 =		e) 5 3 = 125
f) 7 1 =		f) 7 1 = 7

	Practice: Find the value of x	Answers:
	a) 4 x = 64	a) 4 3 = 64
	b) x 3 = 8	b) 2 3 = 8
	c) 10 x = 10,000	c) 10 4 = 10,000
	d) x 3 = 27	d) 3 3 = 27
	e) 13 x = 13	e) 13 1 = 13
	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

	4 6			4 4			4 10
	7			7		=	7

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
		xb

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

	i)	x (x5 )2 x7	=
		(x4 )3

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

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		Powers Refresher
	GRE

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)		−3		1
	x		= 1,000,000

c)5x = 6251

d)x−2 = 2549

e)x−83 = 1

Answers:

a) 5 -2 = 251

1 b) 2 -5 = 32

c) 10 -4 =					1
	10,000
d) (-3) -1 = −					1
					3
e) 4 -3 =	1
	64
f) 11 -1 =		1
	11

Answers:

a)2−7 = 1281

b)		−3		1
	100		= 1,000,000

c)5−4 = 6251

d)5 −2 = 49

7 25

e) 1−83 = 1

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