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

• $2^x + 2^x = 1 \cdot 2^x + 1 \cdot 2^x = (1 + 1) \cdot 2^x = 2 \cdot 2^x = 2^{x + 1}$ – Theo Bendit Feb 6 at 3:10
• $2^x+2^x=2\cdot 2^x=2^1\cdot 2^x=2^{x+1}$ – GReyes Feb 6 at 3:10
• 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 6 at 3:10
• well that was embarrassingly simple! – Max Wen Feb 6 at 5:07
• @john - the issue is that i failed to convert the equation to the form you reference. isn't that obvious? – Max Wen Feb 6 at 5:11

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

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 $$2^{x+1}$$.