1. ## Question about a particular math problem

x^1/4=-3

I recently had this on a math test, and my answer was 81. In order to get this answer, I just 4th rooted both sides.

Can someone explain to me why my answer is wrong? Does it have something to do with the fact that the right side of the equation is a -3?

2. ## Re: Question about a particular math problem

Originally Posted by vp1489
x^1/4=-3
I recently had this on a math test, and my answer was 81. In order to get this answer, I just 4th rooted both sides.
Can someone explain to me why my answer is wrong? Does it have something to do with the fact that the right side of the equation is a -3?
The LHS is non-negative and the RHS is negative.

3. ## Re: Question about a particular math problem

Thank you, but I was hoping someone could explain this to me? I really want to learn and understand the exact reason why it won't work. How come you can't just take the 4th root of both sides to get the answer?

Thank you for the help! I really appreciate it.

4. ## Re: Question about a particular math problem

Hi, I think I can help. When mathematicians write something like:

$\displaystyle x^\frac{1}{4}\ =\ -3$

what they are really saying is "x is the number such that the positive real fourth root of x equals negative three." In other words, 81 does have a fourth root of -3 (it also has the fourth roots 3i and -3i, if you have ever dealt with imaginary numbers), but it is not the "positive real fourth root." Thus, there is no solution to the problem you stated. This is just like when you take the square root of something:

$\displaystyle \sqrt{4}\ =\ 4^\frac{1}{2}\ =\ 2$

It is assumed that we mean the positive real square root, not the negative one. This is called the "principal value," and it's just an arbitrary mechanism that mathematicians agree on so that we are all using the same notation and so that we have to be more specific about what we mean. i.e. If you want the negative square root then you should write the negative square root, and if you want the positive square root then you write the positive square root.