exponents
DESCRIPTION
TRANSCRIPT
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Powers of Real Numbers(Exponents)
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Exponents represent repeated multiplication. For example,
Introduction
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More generally, for any non-zero real number a and for any whole number n,
Introduction
In the exponential expression an, a is called the base and n is called the exponent.
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a2 is read as ‘a squared’. a3 is read as ‘a cubed’. a4 is read as ‘a to the fourth power’. ... an is read as ‘a to the nth power’.
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Caution!
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Caution!
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Properties of Exponents
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Example:
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Properties of Exponents
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Example:
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Properties of Exponents
Homework.
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Example:
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Some Definitions of Exponents
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Properties of Exponents
Homework.
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Example:
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Properties of Exponents
Homework.
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Example:
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Properties of Exponents
Homework.
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Example:
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Properties of Exponents
1. All powers of a positive real number a are positive, i.e. for a ∈ R, a > 0, and n ∈ Z,
an > 0. 2. The even powers of a negative real number a are positive, i.e. for a ∈ R, a ≠ 0 and n ∈ Z,
(–a)n = an (if n is an even number).3. The odd powers of a negative real number a are negative, i.e. for a ∈ R, a ≠ 0 and n ∈ Z,
(–a)n = –an (if n is an odd number)
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Example:
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Example:
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Properties of Exponents
The terms of an expression which have the same base and the same exponent are called like terms. We can add or subtract like terms.
(x ⋅ an) + (y ⋅ an) + (z ⋅ an) = (x + y + z) ⋅ an (a ≠ 0)
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Example:
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Let a ∈ R – {–1, 0, 1} (a is a real number other than –1, 0 and 1).
If am = an then m = n.
Exponential Equations
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2x = 16
3x+1 = 81
22x + 1 = 8x – 1
Examples:
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Exercises: