Exponentiation, Exponent Power EC1-E1100-I
- há 5 anos
To be able to store math information to solve complex exercises, you must understand the basics of math. And for that you should not be afraid to read mathematical notation.
Check back as often as you need to learn what is being shown.
Let "a" be a number that belongs to the set of real numbers, and let "n" be a number that belongs to the naturals.
Remember that Natural is the set of nonnegative integers, in which case we take 0 as a natural number, so the number “n” belongs to this set.
And "a" belongs to the set of real numbers, which contains the natural, integer, fractional, and irrational numbers.
With these values we can define that the number "a" raised to "n", when "n" is equal to zero, is equal to 1. That is any number raised to 0 equals 1. Even the 0 raised to 0 is equal to 1.
The number "a" raised to "n" is equal to "a" raised to "n" minus 1, this value multiplied by "a" for all "n", where "n" is greater than or equal to 1.
If you found it very strange, don't be afraid, keep watching.
We know that "a" raised to 0 is 1. According to the formula if "n" equals 1, we have that "a" raised to 1 equals "a" "n" minus 1, but "n" is 1, so 1 minus 1 is 0. We have "a" raised to zero, every number raised to 0 is 1. According to the formula we have to multiply it by "a", so "a" raised to 1 is "a".
And "a" raised to 2,
If we have "a" raised to 2, this is equal to "a" raised to 2 minus 1, times "a". We have 2 minus 1 is 1, so we saw that "a" raised to 1 is "a", so we have "a" times "a".
If we have "a" raised to 3, we have "a" raised to 3 minus 1, which is 2, we saw that "a" raised to 2 is "a" times "a", so "a" raised to 3 is "a "times" a "times" a ".
This gives you a logical understanding of the power of natural exponent power.
Check back as often as you need to learn what is being shown.
Let "a" be a number that belongs to the set of real numbers, and let "n" be a number that belongs to the naturals.
Remember that Natural is the set of nonnegative integers, in which case we take 0 as a natural number, so the number “n” belongs to this set.
And "a" belongs to the set of real numbers, which contains the natural, integer, fractional, and irrational numbers.
With these values we can define that the number "a" raised to "n", when "n" is equal to zero, is equal to 1. That is any number raised to 0 equals 1. Even the 0 raised to 0 is equal to 1.
The number "a" raised to "n" is equal to "a" raised to "n" minus 1, this value multiplied by "a" for all "n", where "n" is greater than or equal to 1.
If you found it very strange, don't be afraid, keep watching.
We know that "a" raised to 0 is 1. According to the formula if "n" equals 1, we have that "a" raised to 1 equals "a" "n" minus 1, but "n" is 1, so 1 minus 1 is 0. We have "a" raised to zero, every number raised to 0 is 1. According to the formula we have to multiply it by "a", so "a" raised to 1 is "a".
And "a" raised to 2,
If we have "a" raised to 2, this is equal to "a" raised to 2 minus 1, times "a". We have 2 minus 1 is 1, so we saw that "a" raised to 1 is "a", so we have "a" times "a".
If we have "a" raised to 3, we have "a" raised to 3 minus 1, which is 2, we saw that "a" raised to 2 is "a" times "a", so "a" raised to 3 is "a "times" a "times" a ".
This gives you a logical understanding of the power of natural exponent power.