Please be clear with the expressions.
Here we assume
f(x)=(1/3) sqrt(x)
A scale factor is a multiplier applied to a parent function.
If the parent function is f(x), and
g(x)=a*f(x), then a is a scale factor.
Assuming the parent function is sqrt(x), and f(x)=(1/3) sqrt(x)
then the scale factor is (1/3).
[note]
if f(x) is a cube root, then write
f(x)=cube root(x), or f(x)=x^(1/3).
the exponentiation sign ^ is very useful.