Transformation. Take n out of a root

Question

Im kinda confused. If n is always > 0

$$ (n-a)^{\frac{x}{y}} = n*(1-\frac{a}{n})^{\frac{x}{y}} $$

is that true? Because there were some transformations in recent answers to my threads where I did that.

Answer 1

You have the right idea, but you missed one point. the $n$ inside the parentheses is also affected by the outside exponent. What we really have is: $$ \large(n-a)^{\frac{x}{y}}\\ \large\left(n\left(1-\frac{a}{n}\right)\right)^{\frac{x}{y}}\\ \large\left(n^\frac{x}{y}\left(1-\frac{a}{n}\right)^\frac{x}{y}\right) $$