What is the problem with the first equation? I know the square root of negative one is negative one so how is the first line possible?
$$(-1)^{1/3}=(-1)^{2/6}=\sqrt[6]{-1}^2=1$$
$$(-1)^{1/3}=\sqrt[3]{-1}=-1$$
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Welcome to MSE. Please use MathJax to format your posts. – Robin Jun 02 '23 at 08:04
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2Did you mean to write $\sqrt[6]{(-1)^2}$ in the first displayed equation? The rules of exponents apply to positive real numbers. – N. F. Taussig Jun 02 '23 at 08:07
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1"I know the square root of negative one is negative one". Firstly, this is incorrect. $\sqrt{-1}=i \neq -1$. – Robin Jun 02 '23 at 08:10
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@N.F.Taussig Points all out the bottleneck in this seemingly problematic relation. Rules of exponents apply to positive real numbers – Surb Jun 02 '23 at 08:14
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$a^{m/n}=\sqrt[n]{a^m}$ is not universal rule, it has some applicability limits, my book says it is applicable for $a>0, \frac{m}{n}\in \mathbb{Q}$ – Ivan Kaznacheyeu Jun 02 '23 at 08:30