martin-gay, beginning algebra, 5ed 33 exponents that are natural numbers are shorthand notation for...
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Martin-Gay, Beginning Algebra, 5ed 33
Exponents that are natural numbers are shorthand notation for repeating factors.
34 = 3 • 3 • 3 • 3
3 is the base
4 is the exponent (also called power)
Note by the order of operations that exponents are calculated before other operations.
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Martin-Gay, Beginning Algebra, 5ed 44
Evaluate each of the following expressions.
34 = 3 • 3 • 3 • 3 = 81
(–5)2 = (– 5)(–5) = 25
–62 = – (6)(6) = –36
(2 • 4)3 = (2 • 4)(2 • 4)(2 • 4) = 8 • 8 • 8 = 512
3 • 42 = 3 • 4 • 4 = 48
Example:
a)
b)
c)
d)
e)
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Martin-Gay, Beginning Algebra, 5ed 55
Simplify each of the following expressions.
32 · 34 = 36= (3 · 3) · (3 · 3 · 3 · 3) = 729
= 32+4
Example:
32 · 34 = 36 = 729
x4 · x5 = x4+5
z3 · z2 · z5 = z3+2+5
(3y2)(– 4y4) = 3 · y2 (– 4) · y4 = 3(– 4)(y2 · y4) = – 12y6
= x9
= z10
a)
b)
c)
d)
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Martin-Gay, Beginning Algebra, 5ed 66
i) m
m nn
xx m n
x
1ii)
m
n n m
xn m
x x
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Martin-Gay, Beginning Algebra, 5ed 77
Simplify the following expressions.
2
74
3
9
ab
ba 533 ba))((3 2714 ba4 7
2
9
3
a b
a b
Example:
3
5
w
w 5 3
1
w 2
1
w
a)
b)
c)
d)
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Martin-Gay, Beginning Algebra, 5ed 88
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Martin-Gay, Beginning Algebra, 5ed 99
Simplify each of the following expressions.
(23)3 = 29 = 512
(x4)2 = x8
= 23·3
= x4·2
Example:
a)
b)
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Martin-Gay, Beginning Algebra, 5ed 1010
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Martin-Gay, Beginning Algebra, 5ed 1111
a)
b)
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Martin-Gay, Beginning Algebra, 5ed 1212
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Martin-Gay, Beginning Algebra, 5ed 1313
a)
b)
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Martin-Gay, Beginning Algebra, 5ed 1414
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Martin-Gay, Beginning Algebra, 5ed 1515
a)
b)
c)
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Martin-Gay, Beginning Algebra, 5ed 1616