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.
