The last two digits of 62005 are ___.

Hi Pulkit,
Am I missing something? The last two digits of 62005 are 05

Hi Pulkit,

$$6^{2005}$$: Consider the powers of 6:

$$6^1$$ ends in 06, $$6^2$$ ends in 36, $$6^3$$ ends in 16, $$6^4$$ ends in 96, $$6^5$$ ends in 76, $$6^6$$ ends in 56, $$6^7$$ ends in 36, $$6^8$$ ends in 16, $$6^9$$ ends in 96, $$6^{10}$$ ends in 76, $$6^{11}$$ ends in 56, and so on. There is a cycle of 5 starting with the 4th power of 6. So, the last two digits of $$6^{2005}$$ are 76.