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) $0^{417}$ \[ \begin{array}{l} 1^{2}=1 \times 1=\square=0 \times 0= \\ 1^{3}=1 \times 1 \times 1=\square \\ 1^{4}=1 \times 1 \times 1 \times 1=\square= \\ 0^{3}=0 \times 0 \times 0= \\ 0^{4}=0 \times 0 \times 0 \times 0= \end{array} \]

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 ：\[\boxed{0^{417} = 0}\]