Question

proove that 4n is never end with zero for any rational number

Answer 1

we want 
4n =0 for any rational number
4n=0
n=0/4
n=0, which is not a rational number
so that 4n never end with zero for any rational number.
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Answer 2

4n=(2×2)n=2n.2n
if the no. 4n for any natural no. end with digit 0 then it will be divisible by 5. that it is the prime factorisation of 4n contain 5 as a factor but it is not possible because 4n=(2×2)=2n.2n. so,by fundamental theorem of arithemetic . show that there are no.s of other prime factor of 6n. so,no. of natural no.s for which 6n end with the digit 0.


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