Fundamentals of potentiation
Código CM02-E0001-I
VIEW:417 DATA:2020-03-20
When we have numbers multiplying, we can use a mathematical mechanism that facilitates the calculation, which is the potentiation. So, if we have 2 times 2, we can write that each value has a number 1 in the exponent. And so we add the exponents. So, 2 to 2 is 4, which is 2 times 2. When we have 2 as a divisor, then the exponent value is -1. If we put 2 times 1 divided by two, we have 2 raised to 1, times 2 raised to minus 1. We then have 2 raised to 1 minus 1, which is zero. Note that 2 divided by 2 is 1, in fact every number divided by itself is 1, so every number raised to 0 is 1, because when the exponent is zero, it represents that the number is being divided by itself.
So, be any number when this number is raised to 0 the result is 1.
We can now do some proof of mathematical properties.
Let it be 2 times 2, then we have that there is an exponent 1 over each value 2, and so we can add the exponents, and we have 2 raised to two. We know that all numbers can be multiplied by 1, that the value does not change. We also know that any number divided by itself results in a value of 1. So 1 can become 2 divided by two, again every number has an exponent 1. So, we can put 2 raised to 2 divided by two, times 2. Knowing that when you are dividing the exponent it becomes negative. The exponent of 2 raised to 2 can be subtracted by the exponent you are dividing. Generating 2 times 2. See that the mathematical proof may seem unnecessary, but understanding it makes you understand the reason for things.
If we have 0 raised to 3, we have 0 times 0 times 0 which is equal to 0.
But if we have 0 raised to 0, we have the value of 1. That would be 0 divided by 0. But 0 divided by 0 has no logic. Zero cannot be a divisor. So why is 0 raised to 0 is 1? Remember that 2 divided by 2 is 1, and 1 divided by 1 is 1, but if we divide 0.5 by 0.5? the value is 1, what if we divide a very small value by that very small value? The value is 1. So, if we divide by an infinitely small value, by an infinitely small value, the value is one. Now, an infinitely small value is almost zero. So for simple calculations, we define that 0 raised to 0 is 1. But if we are really judicious, and we wish not to imagine the infinitely small as 0, but 0 itself, then 0 raised to 0 does not exist.
But by mathematical convention, in simple calculations we have 0 raised to 0 is 1.
Thus, in general, an "a" raised to a number "n" is n times that number multiplied by itself.
So, be any number when this number is raised to 0 the result is 1.
We can now do some proof of mathematical properties.
Let it be 2 times 2, then we have that there is an exponent 1 over each value 2, and so we can add the exponents, and we have 2 raised to two. We know that all numbers can be multiplied by 1, that the value does not change. We also know that any number divided by itself results in a value of 1. So 1 can become 2 divided by two, again every number has an exponent 1. So, we can put 2 raised to 2 divided by two, times 2. Knowing that when you are dividing the exponent it becomes negative. The exponent of 2 raised to 2 can be subtracted by the exponent you are dividing. Generating 2 times 2. See that the mathematical proof may seem unnecessary, but understanding it makes you understand the reason for things.
If we have 0 raised to 3, we have 0 times 0 times 0 which is equal to 0.
But if we have 0 raised to 0, we have the value of 1. That would be 0 divided by 0. But 0 divided by 0 has no logic. Zero cannot be a divisor. So why is 0 raised to 0 is 1? Remember that 2 divided by 2 is 1, and 1 divided by 1 is 1, but if we divide 0.5 by 0.5? the value is 1, what if we divide a very small value by that very small value? The value is 1. So, if we divide by an infinitely small value, by an infinitely small value, the value is one. Now, an infinitely small value is almost zero. So for simple calculations, we define that 0 raised to 0 is 1. But if we are really judicious, and we wish not to imagine the infinitely small as 0, but 0 itself, then 0 raised to 0 does not exist.
But by mathematical convention, in simple calculations we have 0 raised to 0 is 1.
Thus, in general, an "a" raised to a number "n" is n times that number multiplied by itself.
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Tags
Potentiation, mathematics, radication, elevation