In maths, there are a few basic items that need to be addressed correctly before learning carries meaning.
One of them is the understanding of the function Power or the Exponential.
When you see the expression y = 2k, what do you understand?
Is it 2 multiplied by k?
Or is it 2 multiplied k times?
This is a very common mistake or misconception by students.
2k means 2 multiplied by k times. (or 2 to the power of k).
2 to the power of 4 means 2 x 2 x 2 x 2, which written in the exponential form, becomes 24.
When this is clear, you will know that 2 x 2k is not 4k.
Which is yet another common mistake!
Then, what is this 2 x 2k?
The answer is simply 21 x 2k = 21+k.
This answer makes use of the Product Law of the index property.
To make sure you understand what I mean here, let's do another example.
5 x 23 = ?
It is not 103 !
It is 5 x ( 2 x 2 x 2) ==> 5 x 8 = 40.
OK? Should be fine now, right?
Do not make this unnecessary mistake. 2k is NOT 2 x k.
Bid farewell to this common mistake and move on..... Cheers!