If I have a problem like 3^-2
where the square root is negative, how do I solve it?

Question

If I have a problem like 3^-2
where the square root is negative, how do I solve it?

anonymous · Answer

Recall : a^-b=1/a^b

kropot72 · Answer

3^-2 = 1/3^2 = 1/9

anonymous · Answer

How does it equal 1/3^2?

anonymous · Answer

I think it is just a definition... mathematicians decide that that's how it will be thought of, and it also happens to work with all the rules, so it is good...

anonymous · Answer

You have to wonder what does 3^-2 even mean, physically? 3^2 is easy to attach some meaning in geometry. But I think 3^-2 is slightly more strange. but 3^-2 = 1/3^2 works out well.

kropot72 · Answer

Put 3^-2 over 1:
3^-2/1
Then multiply numerator and denominator by 3^2 remembering that (3^-2)*(3^2)=3^0 = 1.
((3^-2)*(3^2))/3^2 = 1/3^2

anonymous · Answer

Thanks to all that answered. Wish I could've given you all best answer :\

kropot72 · Answer

You're welcome :)