If $2$ divides a number $a$, does $2^n$ divide $a$ ? $n$ is any integar

Question

If $2$ divides a number $a$, does $2^n$ divide $a$ ? $n$ is any integer.

This seems to be true for me, but I just want to make sure it applies for all numbers.

example

if a = 137

2 does not divide 137 4 does not divide 137 8 does not divide 137 and so on

Answer 1

$2$ divides $4$

$2\cdot 4=8$ does not divide $4$

Over and Done!!

Answer 2

Edit: question was changed again, my answer is no longer valid.

Yes, if a divides b then a divides the multiples of b.

Consider b/a = c, where c is a whole number. Take any number d, and multiply it by b. This gives us bd. By our formula early, this means bd/a = dc, where dc is the product of two whole numbers 9i.e, another whole number). This is true for any a, b and d where a divides b.

Answer 3

Do you now mean

does $2^n$ divide $a^n$?

Let $a=2b$, then $a^n=(2b)^n=2^nb^n$