The remainder when ((64)^(64))^(64) is divided by 7 is equal to

Question

The remainder when ${((64{)}^{(64)})}^{(64)}$ is divided by 7 is equal to

Accepted Answer

$$\begin{aligned}
&\begin{aligned}
& 64^{64} \Rightarrow(63+1)^{64}=63 \lambda+1 \
& 64^{664^{64}} \Rightarrow(63+1)^{64^{64}} \
& 63 \lambda_1+1
\end{aligned}\
\&\text { Required remainder when divided } 7 \text { is } 1 \text {. }
\end{aligned}$$

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