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Exponents by Mind Map: Exponents
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Exponents

Degree

Polynomials

Repeated Multiplication

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

Logarithms

Inverse of Exponents

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

Laws

Multiplication

Division

Power of a Power

Power of a Product

Power of a Quotient

Integer Exponents

Alternate Notations

positive

negative

0

Rational Exponents

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

Complex Exponents

Trigonometric Functions

e^(x+iy)

Repeated Division

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

Exponential Function

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

Exponential Decay

Exponential Growth

Origins

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

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"

Real Exponents

Composition of Functions

Exponentiation as repeated composition of functions

Special Bases

10

2

16

8