One of them is the understanding of the function Power or the Exponential.

When you see the expression y = 2

^{k}, 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.

2

^{k}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 2

^{4}.

When this is clear, you will know that 2 x 2

^{k}is not 4

^{k}.

Which is yet another common mistake!

Then, what is this 2 x 2

^{k}?

The answer is simply 2

^{1}x 2

^{k}= 2

^{1+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 2

^{3}= ?

__Solution__:

It is not 10

^{3}!

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. 2

^{k}is NOT 2 x k.

Bid farewell to this common mistake and move on..... Cheers!

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