Question

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

Answer 1

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

Answer 2

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

Answer 3

How does it equal 1/3^2?

Answer 4

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...

Answer 5

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.

Answer 6

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

Answer 7

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

Answer 8

You're welcome :)