Question
Express the following in power notation: $\frac{-1}{128}$
✓
Answer
$\frac{-1}{128}=\frac{(1\times1\times1\times1\times1\times1\times1)}{2\times2\times2\times2\times2\times2\times2 }$
$\begin{array}{c|c} 2 & 128 \\ \hline 2 & 64\\ \hline2&32\\ \hline2&16\\ \hline2&8\\ \hline2&4\\ \hline2&2\\ \hline&1 \end{array}$ $=\frac{(-1)\times(-1)\times(-1)\times(-1)\times(-1)\times(-1)\times(-1)}{2\times2\times2\times2\times2\times2\times2}$
$=\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\\\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)$
$=\Big(\frac{-1}{2}\Big)^7$
$\begin{array}{c|c} 2 & 128 \\ \hline 2 & 64\\ \hline2&32\\ \hline2&16\\ \hline2&8\\ \hline2&4\\ \hline2&2\\ \hline&1 \end{array}$ $=\frac{(-1)\times(-1)\times(-1)\times(-1)\times(-1)\times(-1)\times(-1)}{2\times2\times2\times2\times2\times2\times2}$
$=\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\\\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)\times\Big(\frac{-1}{2}\Big)$
$=\Big(\frac{-1}{2}\Big)^7$
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