<s>[INST] Variable Exponents Question If $a,b$ and $c$ are different positive integers and $2^a\cdot2^b\cdot2^c =64$ then  $2^a+2^b+2^c$=?
This is so far my work: I got $2^a\cdot2^b\cdot2^c=2^6$ then $abc=6$ is this so far in the right track?
 [/INST] Note that
$2^a\cdot2^b\cdot2^c=2^{a+b+c}$ and $64=2^6$.
You know that $2^a\cdot2^b\cdot2^c=64$, then you have that $2^{a+b+c}=2^6$, and from this you conclude that $a+b+c=6$.
Solution $(a,b,c)= (1,2,3)$, therefore $2^a+2^b+2^c= 2^1+2^2+2^3=2+4+8=14$.
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