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Exponents
by Justin Acierto
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Exponents

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Degree

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Polynomials

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Repeated Multiplication

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a^n = a x a x a x ... x a - n times, where n is a natural number

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Logarithms

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Inverse of Exponents

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y = logb(x) <=> b^y = x

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Laws

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Multiplication

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Division

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Power of a Power

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Power of a Product

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Power of a Quotient

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Integer Exponents

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Alternate Notations

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positive

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negative

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0

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Rational Exponents

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a^(1/n) = nth root of a

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Complex Exponents

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Trigonometric Functions

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e^(x+iy)

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Repeated Division

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a^-n = 1/(a x a x a x ... x a) - n times, where n is a natural number

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Exponential Function

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F(x) = ab^x, a: coefficient, b: base

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Exponential Decay

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Exponential Growth

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Origins

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From the latin "exo-" meaning "out of and "ponere" meaning place.

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First introduced by Michael Stifel in 1544 in "Arithmetica Integra" mentioning that "3 is the exponent of 8 and 5 is the exponent of 32"

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Real Exponents

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Composition of Functions

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Exponentiation as repeated composition of functions

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Special Bases

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10

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2

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16

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8

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