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I know that $2^x$+$2^x$=$2^{x+1}$ but I can not explain why. Googling returns too much information about the situation involving variable in the base. Can someone explain? A link to a reference would be sufficient. Thanks

Max Wen
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    $2^x + 2^x = 1 \cdot 2^x + 1 \cdot 2^x = (1 + 1) \cdot 2^x = 2 \cdot 2^x = 2^{x + 1}$ – Theo Bendit Feb 06 '19 at 03:10
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    $2^x+2^x=2\cdot 2^x=2^1\cdot 2^x=2^{x+1}$ – GReyes Feb 06 '19 at 03:10
  • I'm not quite sure what the issue is. Note that $a^{x + 1} = a \times a^x$ for any $a$, including $a = 2$. – John Omielan Feb 06 '19 at 03:10
  • well that was embarrassingly simple! – Max Wen Feb 06 '19 at 05:07
  • @john - the issue is that i failed to convert the equation to the form you reference. isn't that obvious? – Max Wen Feb 06 '19 at 05:11
  • @MaxWen I thought it was due to what I stated, but I've run into many cases where something might seem fairly "obvious" to me but it doesn't to somebody else, and vice versa. Thus, I've found it's usually better to ask to make sure instead of making assumptions. – John Omielan Feb 06 '19 at 05:15

2 Answers2

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$2^x+2^x=2\cdot 2^x=2^{x+1}$.

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I think the others hit the nail in the head, however, I would just like to add the following general statement.

$$x^a*x^b=x^{a+b}$$

In our case, we have the expression:

$$2^x+2^x$$ Which can be rewritten as the equivalent expression:$$2(2^x)$$

Notice that we can apply our general statement to this as follows: $$2^1*2^x$$

Hence, you just "add" the exponents together to get $2^{x+1}$.

Gnumbertester
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