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BruceW

Homework Helper

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## Main Question or Discussion Point

I understand the basics of raising numbers to powers of whatever, but i've been wondering:

When you square a number then square root it, you end up with plus or minus the original number. (i.e. 5 times 5 gets 25, then root gets 5 or -5). But using the rules of raising numbers to powers of other numbers:

(5^2)^0.5=5^1

And i would assume 5^1=just 5, not -5. But the left-hand-side of the equation gives 5 or -5.

Another example: 2^2=2^(4/2)=(2^4)^0.5=16^0.5= 4 or -4

But surely 2^2=4 and not -4

So there seems to be a contradiction. Is there some rule that defines when there is an uncertainy in the sign of the number?

When you square a number then square root it, you end up with plus or minus the original number. (i.e. 5 times 5 gets 25, then root gets 5 or -5). But using the rules of raising numbers to powers of other numbers:

(5^2)^0.5=5^1

And i would assume 5^1=just 5, not -5. But the left-hand-side of the equation gives 5 or -5.

Another example: 2^2=2^(4/2)=(2^4)^0.5=16^0.5= 4 or -4

But surely 2^2=4 and not -4

So there seems to be a contradiction. Is there some rule that defines when there is an uncertainy in the sign of the number?