You have not provided a list of possible equivalents to (4/9)(1/2)^x. But you can still try to simplify (4/9)(1/2)^x.
Start with (1/2)^x. This is the same as 1^x
-------
2^x
Now multiply both sides by (4/9):
4(1)
(4/9)(1/2)^x = ---------
2^x
or 4
--------
2^x
You could also write this as
2 (2) 2^1
---------- = 2 -------- = 2*2^(1-x) or 2[2^(1-x)]
2^x 2^x
