- #1

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- 2

I am a bit confused about definitions rules. I can have more questions but for now I want to ask only one question:

Let us say I have a number: [itex]\sqrt[6]{3x3x3x3x3x3}[/itex]

3x3x3x3x3x3 is equal to both 27^2 and (-27)^2. But If I write these two expressions separately I can get different results:

[itex]\sqrt[6]{27^2}[/itex]=27^(2/6)=27^(1/3)=3

[itex]\sqrt[6]{(-27)^2}[/itex]=(-27)^(2/6)=(-27^1/3)=-3

I know the true answer is 3 but I wonder which step is accepted wrong and why? Is there a definition avoiding me doing one of the wrong steps I did?