Find the values of x when,
x raised to the power root x = x
raised to the power x whole under
root.
To find the values of x in the equation x^(√x) = (x^x)^(1/x), we can start by simplifying both sides of the equation.
For the left side of the equation, x^(√x), we need to express the exponent (√x) in terms of x. One way to do this is to rewrite (√x) as x^(1/2). So the left side becomes x^(x^(1/2)).
Now, let's simplify the right side of the equation, which is (x^x)^(1/x). We can simplify this by applying the exponent rule which states that (a^b)^c = a^(b*c). Therefore, (x^x)^(1/x) simplifies to x^(x * (1/x)) = x^(x/x) = x^1 = x.
Now our equation becomes x^(x^(1/2)) = x.
Next, we can solve for x by equating the exponents on both sides of the equation. We have x^(1/2) = 1.
To solve this equation, we will raise both sides to the power of 2. We get (x^(1/2))^2 = 1^2. Simplifying this gives us x = 1.
So, the only value of x that satisfies the equation is x = 1.