Why does #2^(x+1) + 2^(x+1) = 2^(x+2)# but #3^(x+1) + 3^(x+1) != 3^(x+2)# ?

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Answer 1 · 2016-04-23T00:20:44

See explanation...

For any #a > 0# we find:

#a^(x+1) + a^(x+1) = 2*a^(x+1)#

Also:

#a*a^(x+1) = a^1*a^(x+1) = a^(1+x+1) = a^(x+2)#

So when #a = 2# we have:

#2^(x+1)+2^(x+1) = 2 * 2^(x+1) = 2^(x+2)#

When #a=3# we have:

#3^(x+1)+3^(x+1) = 2 * 3^(x+1)#