Question
Fill in the blank.$(-2)^{-5}= ......$
✓
Answer
$(-2)^{-5}=\frac{-1}{32}$
$\Big[\text{Since}\Big(\frac{\text{a}}{\text{b}}\Big)^{-1}=\Big(\frac{\text{b}}{\text{a}}\Big)^1\Big]$
$(-2)^{-5}=\Big(\frac{-2}{1}\Big)^{-5}=\Big(\frac{1}{-2}\Big)^5$
$=\frac{(1)^5}{(-2)^5}=\frac{1\times1\times1\times1\times1}{(-2)\times(-2)\times(-2)\times(-2)\times(-2)}$
$=\frac{1}{-32}$
$\Big[\text{Since}\Big(\frac{\text{a}}{\text{b}}\Big)^{-1}=\Big(\frac{\text{b}}{\text{a}}\Big)^1\Big]$
$(-2)^{-5}=\Big(\frac{-2}{1}\Big)^{-5}=\Big(\frac{1}{-2}\Big)^5$
$=\frac{(1)^5}{(-2)^5}=\frac{1\times1\times1\times1\times1}{(-2)\times(-2)\times(-2)\times(-2)\times(-2)}$
$=\frac{1}{-32}$
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