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Exponents
by Justin Acierto
# 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

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Number of roots, Real, Complex

a^x * a^y = a^(x+y)

a^x / a^y = a^(x-y)

(a^x)^y = a^(x*y)

(a*b)^y=a^y*b^y

(a/b)^y = (a^y)/(b^y)

Scientific Notation, Must have exactly one significant digit before the decimal

Engineering Notation, exponents for the powers of ten are multiples of 3 to coincide with the metric prefixes

a^0 = 1

sin(z)=(e^i*z - e^-i*z)/2i

cos(z)=)e^i*z + e^-i*z)/2

e^(x+i*y)=e^x * (cos(y) + i*sin(y))

real portion e^x is magnitude

imaginary portion e^iy is direction

b < |1|, reflection in y-axis

a < 0, reflection in x-axis

if a > 0, b > 1, Domain : x e R, Range : y > 0 , y e R, No x-intercepts, y intercept at (0,1), Asymptote @ y = 0

Half-Life

Draining of electric charge from a capacitor over time with a constant load

Intensity of EM radiation inside an absorbing medium as a function of distance from the surface

Compound Interest

Moore's Law for transistors

Nuclear Reaction

Standard Place Value; Decimal Number system

Binary Number System

Hexadecimal Number System

Octal Number System