Series of accumulated products.
Definition of powers
Of ferman: Fernando Mancebo Rodriguez--- Personal page.

You can see many of my works, in the following pages:

COSMIC and ATOMIC MODEL ||| Video: Cosmic and atomic model
Double slit and camera obscura experiments: ferman experiment ||| Type of Waves: Questions of Quantum Mechanics
The socurces of gravity. ||| In favour of the cosmos theory of ferman FCM ||| Theory of Everything: summary
Model of Cosmos. ||| Development speed of forces.||| Magnets: N-S magnetic polarity.
Stellar molecules ||| Static and Dynamic chaos||| Inversion or Left-right proof ||| Scheme approach TOE
Chart of atomic measures||| The main foundations of the Cosmos' Structure ||| Unstable particles in accelerators
Short summary atomic model ||| Positive electric charges reside in orbits.||| Mathematical cosmic model based on Pi.
Inexactness principle in observations ||| Einstein and the gravity ||| The Universal Motion ||| Atomic particles
Cosmic Geometry ||| Bipolar electronic: semiconductors ||| Multiverse or multi-worlds||| Light and photons
Quantum explanation of Gravity ||| Real physics versus virtual physics ||| The window experiment
Atomic Density ||| Linkin: Coeficients Lcf Mcf ||| Atomic nuclei structuring: Short summary
Few points about Cosmic Structuring.||| What is Time||| Simultaneity ||| The Cosmic tree ||| The Cosmic entropy
Interesting and short life of neutrons ||| Leptons field ||| Macro Microcosm, the same thing.
Fourth dimension of space.||| The way to get a unity theory||| UHECR Ultra-high-energy-cosmic-rays
Magnetic or entropy forces: types or classes||| Time observation and time emission ||| The universe expansion
Planetary Mechanics : Short summary ||| Easy explanation of the Planetary model||| State and type of Particles
Higgs boson and fields: wrong way ||| The positron proof: main types of magnetic fields ||| The gravity proof
Current state of cosmology ||| Electromagnetic charges: reason and procedure ||| Neutron: The short and interesting life of
Type of Magnetic Forces ||| The big-bang and Universe' expansion ||| Astronomical chart: Astros, asteroids and microids
Certainty Principle: easy explanation ||| Certainty Principle and the Schrodinger's Cat ||| Wave function collapse
Relativity versus QM ||| The non-curvature of space by matter ||| The Master Clock
Ferman's light analysis ||| Cosmos basic elements, summary||| Comparative numbers in double slit experiment
Stars dimensions ||| Orbital situation of electrons ||| Bright cores versus Black holes
Summary of Ferman cosmic vision and models ||| Atomic nuclei similar to stars ||| Stationary time, but not local neither relativist
Neutrinos versus background radiation ||| Saturn says no to Einstein curvature.||| Da: Average density of energy in the cosmos
Gravity versus magnetic fields of force ||| Black holes cannot exist||| Expansion of materials by energy
Particles in accelerators: almost infinite ||| Trans-dimensional or ideal loupe||| 4D of space, time and matter
5D x 6D = Universal motion x time = Cosmic energy ||| The six cosmic dimensions
Neutrinos ||| Nature of light ||| Hydrogen atom ||| Uncertainty principle: test||| Criticism to Quantum M
Invariance Principle of Time ||| Stuffing forces and heat particles||| Physical waves and imaginary waves
Higgs fields and bosons: Imaginary elements||| Higgs bosons predictions||| Exotic particles
Stars as copies of atoms ||| ERF: Energy rebalancing forces||| Big Bang reality
Radial coordinates.||| Physical and mathematical sets theory. | Algebraic product of sets.
Planar angles: Trimetry.||| Fractions: natural portions.||| Cosmic spiral ||| Inverse values of parameters and operation
Equivalence and commutive property of division. ||| Concepts and Numbers. ||| Bend coefficient of curves ||| Mathematical dimensions
Transposition property ||| Accumulated product: Powers ||| Dimensional Geometry: Reversibility
Priority Rule in powers and roots ||| The decimal counter ||| The floating point index ||| Paradoxes in mathematics
Direct formula for Pi: The Squaring Pi. ||| The pyramids of Squaring Pi. ||| Functions of Pi ||| Integration formulas Pi.
Squaring the Circle ||| Cocktail formula for Squaring Pi.||| Orbital coordinates in motion: Summary
Oscillating function: Cartesian oscillators ||| The ciclo as unit of angular speed ||| Squaring circles ruler and compass |||
Video: Squaring circles ruler and compass ||| The number Phi and the circumference.speed |||
The The extended Pi ||| Angles trisection||| Squaring the Circle regarding Phi||| Video of the two squares method
Discusion about the Pi as transcendental number|||: Not transcendental Pi||| The chained sets|||
Properties of equalities in limits||| The Phi right triangles ||| Pi and the Circumscription Theorem
Pi triangle by squaring the circle : Vedeo Pi triangle ||| Squaring Pi demonstration by circumscription Theorem LatexPdf
Doubling the cube ||| Framing the circle ||| Phi and Pi: relation formula
Squaring circle with Phi (to 0.000005 of ideal ruler and compass)||| Sbits: Static and dinamic orbital coordinates
Squaring Pi and the Floating Point
Spherical molecules. ||| Genetic Heredity. ||| Metaphysics: Spanish only. ||| Brain and Consciousness. ||| Type of Genes T and D
Certainty Principle ||| From the Schrodinger cat to the Ferman's birds ||| The meaning of Dreams
Freely economy ||| Theoricles of Alexandria ||| Rainbow table of elements.||| Satire on the Quantum Mechanics
Cancer and precocious aging ||| Hardware and software of Genetics ||| The farmer and the quantum physicist
Dreams and unconscious logical computing ||| Intelligence and logic ||| How our brain and mind work
Andalusian Roof Tile. ||| Rotary Engine. ||| Water motors: Vaporization engines.
Triangular ferman's Houses .||| Pan for frying and poaching eggs ||| The fringed forest
Summary of Hydraulic Chenge Box ||| Ferman fingernails
The Emperor's new clothes and the QM ||| Garbage Triangle: Quantum mechanics, Relativity, Standard theory
Fables and tales of the relativists clocks.||| Nuclei of galaxies.||| Particles accelerators.
Hydrocarbons, water and vital principles on the Earth. ||| Cosmos formula : Metaphysics
Ubiquity Principle of set.||| Positive electric charges reside in orbits.
Chaos Fecundity. Symbiosis: from the Chaos to the Evolution.||| Speed-Chords in galaxies.
The ancient planets Asteron and Poseidon.||| The man and the testosterone.||| Toros say ||| The essence of life
Chaos + symbiosis = evolution ||| Future Cosmology: Satire on Relativity and Quantum Mechanics
The stupid tale of the astronaut that did not age ||| Summary of Ferman cosmic vision and models
Climate due to human activity ||| Humans as herd animals
Video Universal Consciousness||| Who is God ||| Faces of God ||| Web Universal consciousness
Creation: Highlights||| First steps in metaphysics ||| A personal experience
Reason for the Cosmos' creation ||| The essence of life ||| Cosmic Entity: Metaphysics and Physics parameters


Accumulated Product
Series of accumulated products
Powering Series
Definition of Power.

Product between two numbers

The product between two numbers (a x b) will be the result of adding the value of (a) so much times as units (b) has.
Although to multiply, we use tables (memorized) that allow us the direct multiplication without necessity of making the sequential addition, which on the other hand, allows us the multiplication of decimals, fractions, etc.

Accumulated Product:

Accumulated Product will be the product applied to the result of anterior multiplication.
For example, given 3x5x6, where firstly we make the multiplication 3x5 = 15 and later on we make the multiplication 15x6 = 90
The accumulate product have the particularity of been made step by step when not having tables that would allows us to make in a unique operation.
For example, the accumulated product 3x5x6, as we have seen, is not possible to make in alone one operation, but in two accumulative operations.

Series of accumulated products:

Series of Accumulated Products will be when we multiply all the terms (a,b,c, ....) of a series (set or succession) in the order of representation.
For example, the series 3x5x4x2 will be resolved: 3x5 = 15; 15x4 = 60; 60x2 = 120
In the series the total quantity of terms to multiply is defined as degree (n) of the series.
In the anterior example, n=4 mean to be a series of fourth (4) degree.

Powering Series:

Powering series will be when all the terms of the series of accumulated products are equal.
For example, given de series 3x3x3x3x3 when having equal all the terms, it will be a powering series.
In the powering series the first and second terms will also be considered accumulated products by convention.
The powering series can be simplified by mean of a base (a) that represent the repeated term, and by mean of a exponent that represent the degree (n) of the powering series.
To this simplification of the powering series we can name as Power.
For example, given a powering series 3x3x3x3x3, where its simplification o power is 3^5.

Definition of Power :

As for the anterior considerations, the definition of power could be:
"Power is the accumulated product of a series of equal terms."


Very often we find in power form many operation that are not powers really, as in the case of roots.
In the case of a square root, we also can express it in power form with a base (a) and an exponent (1/n), as for example 9^(1/2)
But in this case it is not a power exactly, but its inverse operation, the root; and for this reason we also have to change the sense of seeking, say, here we have the accumulated product (9) of a series of degree (2) and what we have to find is the base (a) that is the root result.
In the case of 9^(1/2) = 3; the resulting 3 will be the base (a) of the accumulated product of the series (9) that was known.
Say, in the roots we seek the base of the accumulated product of the series.

Definition of root

As for the anterior considerations, the definition of roots could be:
"Root of a given accumulated product is and consists in obtaining the base (a) of the series that gives us that accumulated product."

Exponential fractions
It could occur also that we could have an exponent in form of fraction, as for example 4^(3/2).
In this case the operation would be double because we have a accumulated product and two degrees (n,m) to resolve.
Firstly we adjust the accumulated product of (n) degree, and later on with this partial result we proceed to solve the base of the (m) degree.
For example, given 4^(3/2), where firstly we adjust the (n) degree 4^3 = 64 as accumulated product, and later on we adjust the (m) degree as root 64^(1/2) = 8

Methods of powers and roots.
Direct or priority power -3^4, and series power (-3)^4

Direct or priority power will be when the power is applied uniquely on the numeric module, and this way, the module is revolve firstly and later on we apply the sign that the base got.
For example, given -3^4 = -(3x3x3x3) = -81
It will be complete power when we apply the power jointly to the numeric module and sign.
For example, given (-3)^4 = (-3x-3x-3x-3) = +81

Direct or modular root and complete root.

The direct or modular root will when the root is applied alone on the module of the base, and later on, we apply the sign that this base got.
For example, given -81^1/4 = -(81)^1/4 = -3
Complete root will be when the root is applied jointly to module and sign, given in this case imaginary results with even root of negative number.
For example, given (-81)^1/4 = 3i