Question
Express the following in power notation: $\frac{-32}{243}$
✓
Answer
$\frac{-32}{243}=\frac{(-2)\times(-2)\times(-2)\times(-2)\times(-2) }{3\times3\times3\times3\times3}$
$\begin{array}{c|c} 2 & 32 \\ \hline 2 & 16\\ \hline2 &8\\ \hline 2 & 4\\ \hline2 & 2 \\ \hline &1 \end{array}$
$\begin{array}{c|c} 3 & 243 \\ \hline 3 & 81\\ \hline3&27\\ \hline3&9\\ \hline3&3\\ \hline&1 \end{array}$
$=\Big(\frac{-2}{3}\Big)\times \Big(\frac{-2}{3}\Big)\times \Big(\frac{-2}{3}\Big)\times \Big(\frac{-2}{3}\Big)\times \Big(\frac{-2}{3}\Big)$ $=\Big(\frac{-2}{3}\Big)^5$
$\begin{array}{c|c} 2 & 32 \\ \hline 2 & 16\\ \hline2 &8\\ \hline 2 & 4\\ \hline2 & 2 \\ \hline &1 \end{array}$
$\begin{array}{c|c} 3 & 243 \\ \hline 3 & 81\\ \hline3&27\\ \hline3&9\\ \hline3&3\\ \hline&1 \end{array}$
$=\Big(\frac{-2}{3}\Big)\times \Big(\frac{-2}{3}\Big)\times \Big(\frac{-2}{3}\Big)\times \Big(\frac{-2}{3}\Big)\times \Big(\frac{-2}{3}\Big)$ $=\Big(\frac{-2}{3}\Big)^5$
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