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Exponents by
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# Exponents

## Degree

### Polynomials

Number of roots, Real, Complex

## Laws

### Multiplication

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

### Division

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

### Power of a Power

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

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

### Power of a Quotient

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

## Integer Exponents

### Alternate Notations

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

## Complex Exponents

### Trigonometric Functions

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))

### e^(x+iy)

real portion e^x is magnitude

imaginary portion e^iy is direction

## Exponential Function

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

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

### Exponential Decay

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

### Exponential Growth

Compound Interest

Moore's Law for transistors

Nuclear Reaction

## Special Bases

### 10

Standard Place Value; Decimal Number system

### 2

Binary Number System