The shape of a graph of a function with $n$th-roots?

Question

Not just these type of functions:

$$\sqrt[3]{x}=x^{1/3} \;\;\;\text{and} \;\;\; \sqrt[8]{x}=x^{1/8}$$

But also more complicated expressions, like expressions that have $n$th roots inside of $n$th roots, or exponentiation inside of $n$th roots:

$$ \sqrt[5]{\sqrt{x}} \;\;\;\;\;\text{or}\;\;\;\;\; \sqrt[9]{x^{12}} \;\;\;\;\;\text{or}\;\;\;\;\; \sqrt[13]{\sqrt[7]{\sqrt{x}}}.$$

Is there a general idea about the shapes of graphs of such functions? What shapes does a graph take on if you keep adding $n$th roots to the inside of the function, for example going from $\sqrt[7]{x}$ to $\sqrt[7]{\sqrt{x}} \dots$ etc?

Thank you.

Answer 1

x^p when 0

when p>1 look like x^2