evaluate-1-2-3-3-4-5-mod-10-

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Question Number 215 by 123456 last updated on 25/Jan/15

$$\mathrm{evaluate}$$$$1+2^3+3^{4^5}\left(\mathrm{mod}10\right)$$

Answered by prakash jain last updated on 16/Dec/14

$$1+2^3=9$$$$3^{4^5}\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{power}\mathrm{of}9\left(9^{512}\right)\mathrm{so}$$$$\mathrm{units}\mathrm{place}\mathrm{of}{3}^{4^5}\mathrm{is}1.$$$$\mathrm{unit}\mathrm{place}\mathrm{of}1+2^3+3^{4^5}\mathrm{is}0$$$$\mathrm{hence}1+2^3+3^{4^5}\left(\mathrm{mod}10\right)=0$$

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