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270^{270}=10^{270}\times 27^{270}
130^{130}=10^{130}\times 13^{130}

That means 270^{270} ends with  270 zeroes and 130^{130}  ends with 130 zeroes . Notice that the right most non-zero digit is not affected by the first number. The problem reduces to finding the last digit of 13^{130} :

13^{130}\equiv 3^{130}=9^{65}\equiv (-1)^{65}=-1\equiv 9\pmod{10}

Therefore the last non-zero digit of 270^{270}+130^{130} is 9
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