I am having trouble understanding this... I can't remember whose notes this is from, but it is something I printed off this site.

7^4 + 7^7

= 7^4(1+7^3)

=7^4(50)

And

3^4+12^4

=3^4+ (3*4)^4

=3^4(1+4^4)

=3^4(256)

In both instances I am confused with what happens to the one in the second to last step. Wouldn't it be 3^4+3^4(256)? It seems like the 1 just disappears???

Here is a problem I can not solve:

2^x - 2^x-2 = 3(2^13)

x=?

The answer is 15 but I do not understand how to get it. Is there a good guide online or does someone have good notes for exponents? I am lacking in this area and I need it dumbed down.

1. \(7^4+7^7\) --> factor out 7^4 --> \(7^4(1+7^3)=7^4(1+343)=7^4*344\) (so the answer given in your example is not correct);

2. \(3^4+12^4=3^4+(3*4)^4=3^4+3^4*4^4\) --> factor out 3^4 --> \(3^4(1+4^4)=3^4(1+256)=3^4*257\) (so again the answer given in your example is not correct).

A. 9

B. 11

C. 13

D. 15

E. 17

\(2^x - 2^{x-2} = 3*2^{13}\) --> factor out \(2^{x-2}\) --> \(2^{x-2}*(2^2-1)=3*2^{13}\) --> \(2^{x-2}*3=3*2^{13}\) --> \(2^{x-2}=2^{13}\) --> \(x-2=13\) --> \(x=15\).

Answer: D.