Find the last digit of the following numbers: 6^95, 7^95, and 8^95 by using patterns.
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Copy the table. $$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text { Power } & 9^{1} & 9^{2} & 9^{3} & 9^{4} & 9^{5} & 9^{6} & 9^{7} & 9^{8} \\ \hline \text { Evaluate } & ? & ? & ? & ? & ? & ? & ? & ? \\ \hline \end{array} $$ Evaluate the powers of 9 in the table. What pattern do you see for the last digit of each product?
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Copy the table. $$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text { Power } & 9^{1} & 9^{2} & 9^{3} & 9^{4} & 9^{5} & 9^{6} & 9^{7} & 9^{8} \\ \hline \text { Evaluate } & ? & ? & ? & ? & ? & ? & ? & ? \\ \hline \end{array} $$ Make a table like the one shown for powers of $8 .$ Describe any patterns.
Find the last three digits of 9^105, using the Chinese Remainder Theorem.
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