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

(8) 81, base 3

Because 3 is the base, we will take it as a factor for writing 81 in multiplication form.

Thus, we have:

$\begin{array}{cc}3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

⇒ 81 = 3 × 3 × 3 × 3 = 3⁴