There is a way to do it where you look for some type of exponents.. ms.cooper said something about it in class..trying to rememeber... (first post) it had to do with find like 3 to the second then 4 to the second
OK.i think i know how to do this...first you start by doing a couple of the numbers in the series, then look at the ones digit until you find a pattern. You find out how many exponents it took to get to that number (you should know that) then you divide some number by that...
**instead of looking at the number of exponents, look at how many 1s digits the pattern goes through until it restarts... THEN u divide some number by that.
ya you are supposed to look at it and find a pattern for like the first 10 numbers than if you find a pattern you are supposed to divide or do something that makes the pattern true
For the ones digits the pattern is 8, 4, 2, 6. It is a four number pattern, so you could do 2007 divided by 4. There is a remainder of 3, so you count 3 into the pattern.
8 to the first power ones digit is 8 8 to the 2nd power-ones digit is 4 8 to the third power-ones digit is 2 8 to the fourth power-ones digit is 6 8 to the fifth power-ones digit is 8 So you can see there is a pattern of repetition 8,4,2,6 8,4,2,6 8,4,2,6 Since you are looking for the 2007th power that means this repeition of 4 digits repeats 501 times since 2007 divided by 4 is 501 is 501 with a remainder of 3. So the 2007th power will bring you to the 3rd (remainder 3) digit in the pattern. So the answer is 2!
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There is a way to do it where you look for some type of exponents.. ms.cooper said something about it in class..trying to rememeber...
(first post) it had to do with find like 3 to the second then 4 to the second
OK.i think i know how to do this...first you start by doing a couple of the numbers in the series, then look at the ones digit until you find a pattern. You find out how many exponents it took to get to that number (you should know that) then you divide some number by that...
**instead of looking at the number of exponents, look at how many 1s digits the pattern goes through until it restarts... THEN u divide some number by that.
ya you are supposed to look at it and find a pattern for like the first 10 numbers than if you find a pattern you are supposed to divide or do something that makes the pattern true
Consider this...
8 to the first power-ones digit is _
8 to the second - ones digit is __
8 to the third - ones digit is ___
and so on.
For the ones digits the pattern is 8, 4, 2, 6. It is a four number pattern, so you could do 2007 divided by 4. There is a remainder of 3, so you count 3 into the pattern.
Good Hallie.
Hallie has the right idea!!!!!!
this problem is PRECISELY why hashem gave us calculators.
you could do 8 to the power of 2007, but that would take way to long so you can go by the 8,4,2,6 pattern and ADD 3 into the pattern
I think the only thing you have to do is find the answer to the first few exponents and find a pattern
8 to the first power ones digit is 8
8 to the 2nd power-ones digit is 4
8 to the third power-ones digit is 2
8 to the fourth power-ones digit is 6
8 to the fifth power-ones digit is 8
So you can see there is a pattern of repetition 8,4,2,6 8,4,2,6 8,4,2,6
Since you are looking for the 2007th power that means this repeition of 4 digits repeats 501 times since 2007 divided by 4 is 501 is 501 with a remainder of 3. So the 2007th power will bring you to the 3rd (remainder 3) digit in the pattern. So the answer is 2!
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