Carcass wrote:
What is the ones digit of \(3^{23} - 2^{18}\) ?
enter your value Now we know
Ones digit of\(2 ^ {any power}\) = 2,4,8,6 i.e it keeps repeating after every 4 cycle
Ones digit of \(3 ^ {any power}\) = 3,9,7,1 i.e it keeps repeating after every 4 cycle
Now ones digit of \(3^{23}\) = 7 (divide 23/4 , since it repeats after every 4 cycle and the remainder is 3, so we have to consider the third term i.e 7 (3,9,7,1))
Similarly ones digit of \(2^{18}\) = 4 (divide 18/4 , since it repeats after every 4 cycle and the remainder is 2,
so we have to consider the second term i.e 4(2,4,8,6))
Now
the ones digit of \(3^{23} - 2^{18}\) = 7-4 = 3
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