Which value of n in 2^n× 5^n make the unit place as 5

1.	Which value of n in 2^n× 5^n make the unit place as 5
Answer» {tex}\\begin{array}{l}(2\\times5)^{\\mathrm n}=2^{\\mathrm n}\\times5^{\\mathrm n}\\end{array}{/tex}{tex}\\text{=10}^n{/tex}{tex}\\text{If n=0 then 10}^0\\text{=1}{/tex}{tex}\\text{If n>0 then 10}^n\\text{ will end with 0 }{/tex}{tex}\\mathrm{If}\\;\\mathrm n<0\\;\\mathrm{then}\\;10^{\\mathrm n}\\;\\mathrm{ends}\\;\\mathrm{with}1\\;(\\mathrm e.\\mathrm g.\\;0.1,0.01,0.001){/tex}Hence for all values of n, {tex}2^n\\times 5^n{/tex} can never end with 5.

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