If x^2 = √16, then how to calculate the value of 'x' in exponential form? I have done below in the root form
x^2 = √16, x= √(√16), x= √4 =2 Is the method is correct? if correct, please solve this problem in exponential form. I have tried below
x^2 = 16^1/2, x^2 = 4, x^2 = 2^2, x = 2 Am I correct? If correct, can you please solve it in any other methods?
First, you're not quite right, because x could be either +2 or -2, as has been empathized. PLEASE don't forget that; I think some of us may be thinking you are refusing to pay attention, and getting frustrated.
But for the moment, let's suppose you were also told that x>0, so you don't need to worry about that.
As written, x^2 = √16, I would first simplify the right side, so x^2 = 4. Then there are several ways to get to the answer; your way is valid only if you know that x>0! If you don't, then you need to either remember to include the negative case, or use the factoring method you have been shown:
x^2 = 4
x^2 - 4 = 0
(x + 2)(x - 2) = 0
x + 2 = 0 or x - 2 = 0
x = -2 or x = 2
But suppose now that you were given x^2 = √y, where you don't know y, and you are told to solve for x in terms of y, "in exponential form". Then you might do this, using exponents all the way:
x^2 = y^(1/2)
(x^2)^(1/2) = (y^(1/2))^(1/2)
x^(2*1/2) = y^(1/2 * 1/2)
x^1 = y^(1/4)
x = y^(1/4)
Now, in doing this, I assumed that x>0. If I couldn't do that, I would have to be aware that, just as there are two square roots, there are two 1/2 powers (since that means the same thing), so I would do this:
x^2 = y^(1/2)
(x^2)^(1/2) = ±(y^(1/2))^(1/2)
x^(2*1/2) = ±y^(1/2 * 1/2)
x^1 = ±y^(1/4)
x = ±y^(1/4)
(Note that the right side was given as √y, that means only the positive root, so I didn't use ± at the start.)
It would also be possible to express this in terms of factoring, though that is a little more awkward than with numbers.
If you are asking this because of a specific problem you have been given, it will be very helpful if you can quote the problem and tell us the context, so we can be sure what issues matter.