Solving x^(2n) = 1/(2^n) for x

ndevunidt

ndevunidt

Answered question

2022-10-17

Solving x 2 n = 1 2 n for x
What is the principle behind solving for a variable that is raised to another variable? I came across this problem doing infinite sums: I had to solve the equation
x 2 n = 1 2 n
for x. I posed the question in the online forum and the TA said the answer is
x = 1 2 .
I don't see how he got there. If someone could explain how to get from one to the other, I would appreciate it!

Answer & Explanation

Phoebe Medina

Phoebe Medina

Beginner2022-10-18Added 17 answers

x 2 n = ( x 2 ) n = 1 2 n . So if n 0, for x R you have x 2 = 1 2 then x = 1 2 or x = 1 2

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