Question
Express the following as a rational number:
$(-2)^{-5}$
$(-2)^{-5}$
✓
Answer
$(-2)^{-5}=\Big(\frac{1}{-2}\Big)^{5}$
$=\Big(\frac{1\times(-1)}{-2\times(-1)}\Big)^5=\Big(\frac{-1}{2}\Big)^5$
$=\Big(\frac{(-1)\times(-1)\times(-1)\times(-1)\times(-1)}{2\times2\times2\times2\times2}\Big)$
$=\frac{-1}{32}$
$=\Big(\frac{1\times(-1)}{-2\times(-1)}\Big)^5=\Big(\frac{-1}{2}\Big)^5$
$=\Big(\frac{(-1)\times(-1)\times(-1)\times(-1)\times(-1)}{2\times2\times2\times2\times2}\Big)$
$=\frac{-1}{32}$
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