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What is the digit in the tens place when 7^2008 is expressed in decimal notation?

 Jul 21, 2022
 #1
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+1

7^2008 mod10^10==8326964801 - these are the last 10 digits.

 Jul 21, 2022
 #2
avatar+124524 
+1

7^2 = 49

7^3  = 343

7^4 = 2401

7^5 = 16807

7^6 = 117649

7^7 = 823543 

7^8  = 5764801

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7^(2n).....when n is odd, the tens  digit  =  4

7^(2n).....when n is even, the tens digit  = 0

 

7^(2008)  = 7^(2 * 1004)  →   the tens  digit   =   0

 

 

cool cool cool

 Jul 21, 2022

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