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What's 0 to the power of 0?

Presumably, you meant to say that there are no negative square numbers? (and that is easily fixed with imaginary numbers, but let's stick with real numbers for now).

What is 4^{1/2} ? Why?

What is (-4)^{1/2} ? Is there no real solution?

but what happens to the LHS and RHS when you let x = -3 ? Don't we obtain +3 = -3 ?

So what is the value of 3^{π}? Could it be a negative number?

If that's too easy consider (-3)^{π} .

If you were given the expression (x^{2})^{1/2} = x and then set x= -3 then you would have to deduce that +3 = -3.

If you were given the expression (x2)1/2 = x and then set x= -3 then you would have to deduce that +3 = -3.No.

Quote from: Eternal Student on Yesterday at 17:49:40 What is 4^{1/2} ? Why?- - - - - - - Hamdani replied:y=4^{1/2}y=2ory= -2because 22=4and (-2)2=4

Thank You for the Corrections.Just wanted to show you folks a lil something... Screenshot_2021-11-04-00-41-12-800_com.miui.calculator.jpg (116.43 kB . 1080x2156 - viewed 1459 times)Ps - I use a Poco Android Mobile(model) by MI(company).& I find it Strange that a built in default Chinese designed Calculator App is in clear defiance of the all mighty & powerful GooGle.(The damm thing won't even Uninstall, & no I'm Not into Rooting so save that advice for someone else)

Appalling gramme, it should be cannot, not "can't". You also cannot divide by 1 or anything beneath

This is slightly different to the example Sin(0) = Sin(π). You can assign more than one value in the domain of a function to the same value in the Range. However, you cannot assign one value in the domain to more than one value in the Range. ("Many to One" is OK but "One to Many" is not).

But the selection of principal root is just a convention.

Try arcsin(x) = 0

ArcSin is only a well defined function when you restrict the domain of the parent Sine function.

it will be well defined whenever Ln(a) exists.

When does Ln(a) not exist?