What is the remainder when 38^42 is divided by 10? And how

What is the remainder when 38^42 is divided by 10? And how I got two answers of this one is 24 by seperate then divide then fermat little therom and other is 4 by concept of cyclicity

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  • The remainder is 4.
    The last digit of 38 is 8 and lets take a look on the increasing powers of 8. We can see that there is a repeatation after 8^4. 
    So basically what we have to do is to divide 42 by 4 and take out the remainder. So we can see the remaider in this case is 2. So we take 8^2 and it gives us 4 in the one's place of the required digit of 38^42.
    We know that if a number with its one's digit 4 is divided by 10 the remainder is alwaays 4.
    So from here we can conclude the remainder of this problem is 4.
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  • 44
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  • 38^42=(38^21)^2=(.........88)^2
    ans= ..........44
    the last last two digits of the number is 44 and when it is divided by 10 the remainder is 4
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