Copy and complete the calculations below. For each set of calculations, write a sentence to explain the pattern you see.
Use your patterns to work out
a) $1^{417}$
b) $0^{417}$
\[
\begin{array}{l}
1^{2}=1 \times 1=\square=0 \times 0= \\
1^{3}=1 \times 1 \times 1=\square \\
1^{4}=1 \times 1 \times 1 \times 1=\square= \\
0^{3}=0 \times 0 \times 0= \\
0^{4}=0 \times 0 \times 0 \times 0=
\end{array}
\]
Answer
\[\boxed{0^{417} = 0}\]
Step 1 ：\[\begin{array}{l} 1^{2}=1 \times 1=1=0 \times 0=0 \\ 1^{3}=1 \times 1 \times 1=1 \\ 1^{4}=1 \times 1 \times 1 \times 1=1 \\ 0^{3}=0 \times 0 \times 0=0 \\ 0^{4}=0 \times 0 \times 0 \times 0=0 \end{array}\]
Step 2 ：The pattern is that for any power of 1, the result is always 1, and for any power of 0, the result is always 0.
Step 3 ：Using the pattern, we can find the values of $1^{417}$ and $0^{417}$.
Step 4 ：\[1^{417} = 1\]
Step 5 ：\[0^{417} = 0\]
Step 6 ：\[\boxed{1^{417} = 1}\]
Step 7 ：\[\boxed{0^{417} = 0}\]
