Asked by Amy
                7^0 = 1
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
Pattern of ones digit is 1,7,9,3,1,7,9,3...
However, I don't understand how you can find this pattern in the values given above?
            
        7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
Pattern of ones digit is 1,7,9,3,1,7,9,3...
However, I don't understand how you can find this pattern in the values given above?
Answers
                    Answered by
            Amy
            
    Also, the originally problem is finding the ones digit 537^102
and I found out that 7 was a one digit factor
    
and I found out that 7 was a one digit factor
                    Answered by
            Reiny
            
    What the patters is supposed to show is..
in 537^102 you only have to look at what happens to the ones digit
e.g.
537^0 = 1 vs 7^0 = 1
537^1 = 53<b>7</b> vs 7^1 = <b>7</b>7
537^2 = 28836<b>9</b> vs 7^2 = 4<b>9</b>
537^3 = 15785415<b>3</b> vs 7^3 = 34<b>3</b>
537^4 = 8315....<b>1</b> vs 7^4 = 240<b>1</b>
notice the last digit is either
1 , 7, 9, or 3 , and cycles in that pattern
If the exponent is odd ---> not our problem
if the exponent is even and divides by 4, then it end in a 1
if the exponent is even but does not divide by 4, it ends in a 9
our exponent of 102 is even but not divisible by 4, so
537^102 will end in a 9
    
in 537^102 you only have to look at what happens to the ones digit
e.g.
537^0 = 1 vs 7^0 = 1
537^1 = 53<b>7</b> vs 7^1 = <b>7</b>7
537^2 = 28836<b>9</b> vs 7^2 = 4<b>9</b>
537^3 = 15785415<b>3</b> vs 7^3 = 34<b>3</b>
537^4 = 8315....<b>1</b> vs 7^4 = 240<b>1</b>
notice the last digit is either
1 , 7, 9, or 3 , and cycles in that pattern
If the exponent is odd ---> not our problem
if the exponent is even and divides by 4, then it end in a 1
if the exponent is even but does not divide by 4, it ends in a 9
our exponent of 102 is even but not divisible by 4, so
537^102 will end in a 9
                    Answered by
            Amy
            
    Thank you so much! Your explanation was very helpful!
    
                    Answered by
            Reiny
            
    the 2nd line of the e.g.'s should say
537^1 = 53<b>7</b> vs 7^1 = <b>7</b>
    
537^1 = 53<b>7</b> vs 7^1 = <b>7</b>
                    Answered by
            Fitzpatrick
            
    7 xxxxx
    
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