Write each of the following numbers in index form with the given base.

(1) 125, base 5

Because 5 is the base, we will take it as a factor for writing 125 in multiplication form.

Thus, we have:

$\begin{array}{cc}5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$

⇒ 125 = 5 × 5 × 5 = 5³