So I think you mean the '2048' type of mobile game?
If there are 4 tiles. And we start with only blocks of 2. And we assume we can merge any two blocks. (So no need to shuffle two blocks next to eachother).
We need two 2 blocks to create a 4 block. Which is one step. Then again two 2 blocks to create a 4 block which is another step. Then we can merge these two 4 blocks into an 8 block. So 3 steps in total.
You will need a total of x steps to get the 2\^x block. (Assuming all blocks necessary are provided)
If I misunderstood your problem please let me know.