Relearning the rules of exponents and I need help understanding this question in the ETS book. Forgive me if I miss the obvious. I haven’t looked at math in god knows how long…

Quantity A: 2^30 - 2^29 / 2
Quantity B: 2^28

I’ve simplified Quantity A and B as follows:

Quantity A: 2^30
Quantity B: 2^29 + 2^29

Can someone please tell me what law of exponents makes 2^29 + 2^29 = 2^30?

I understand it is not a multiplication otherwise it would be 2^58 – but it’s definitely not this property.

Okay I first of all, please go through the below explanation, I will simplify with an example later:

First of all, let’s say for a variable ‘a’:

a x 1 + a x 1 = a x (1+1) = a x (2) do you agree with this? We just took out a as the common factor of the two. We also know any number ‘a’ can be written as ‘a’ and the product of ‘a’ and 1.

For example: 2 + 2 = 2 x 1 + 2 x 1 = 2 x (1+1) = 4

So we can write 2^29 + 2^29 = 2^29 x (1+1) = 2^29 x 2 = 2^30

You cannot add powers unless they are being multiplied. Let me know if you need further help.