Though it is a really simple question, I am stuck in explaining myself where I break the rules. $$\sqrt{-3}\sqrt{-3} = i^2\sqrt{9}=-3=(-3)^{\frac{1}{2}}(-3)^{\frac{1}{2}} = (-3)^{\frac{1}{2}+\frac{1}{2}}=-3$$ but in the next one, there's something wrong and I do not understand what it is: $$(-3)^\frac{1}{2}(-3)^\frac{1}{2}=((-3)(-3))^\frac{1}{2}=\sqrt{9}=3$$ That is, why cannot I get the product of the bases since I have the same exponent?
Asked
Active
Viewed 10 times
0
-
1Does this answer your question? Why $\sqrt{-1 \times {-1}} \neq \sqrt{-1}^2$? – Brian61354270 Feb 01 '20 at 18:05
-
1rather than thinking of it as you doing something wrong, what this shows you is that the "usual/familiar" rules of exponents only have a limited domain of validity (eg when the numbers in question are all positive). I suggest you take a look at each of those theorems and look at the HYPOTHESES, not just the formula – peek-a-boo Feb 01 '20 at 18:06
-
Oh, I see, the thing is that, first, I should take the exponent, and then I can multiply. So in my example that's exactly what I broke.. – mur_tm Feb 01 '20 at 18:19