Question

(b) Based on the evidence in part (a), make a conjecture about the order of ${\mathit{a}}^{\mathbf{k}}$ when $\left|\mathit{a}\right|=\mathbf{n}$.

Short answer

For all $1\le k<n$ then $\left|a^k\right|=\frac{12}{\left(\mathrm{k}\mathrm{,}\mathrm{n}\right)}$ .

Step-by-step solution

Determine given functions of part (a)

Consider the given functions,

$a\in G$and $\left|a\right|=12$.

Determine conjecture order

Given that, $a^k$, when $\left|a\right|=n$, then the order is,

For all $1\le k<n$then $\left|a^k\right|=\frac{12}{\left(\mathrm{k}\mathrm{,}\mathrm{n}\right)}$.