Question

If $36=6\times 6=6^2$, then expressed $\frac{1}{36}$as a power with the base 6 is _________.

Fill in the blank to make the statement true.

Answer 1

Express $\frac{1}{36}$as a power with base $6$

$\begin{array}{rcl}\therefore \frac{1}{36}& =& \frac{1}{6}\times \frac{1}{6}\\ & =& {\left(\frac{1}{6}\right)}^2\\ & =& {\left(6^{-1}\right)}^2\\ & =& 6^{-2}\end{array}$

Hence, $\frac{1}{36}$ is expressed as $6^{-2}$.