I got this one right but how do I do it without multiplying

Question

I got this one right but how do I do it without multiplying out the freaking numbers?

ps_dahiya · Answer

No need to multiply. Just solve the given equation.

2^5 + 2^5 = (2^5) * (1+1) = (2^5) * 2 = 2^6
3^5 + 3^5 + 3^5 = (3^5) * (1+1+1) = (3^5) * 3 = 3^6

Hence C

jamesrwright3 · Answer

I never learned that theory...
Where did you pick that up from? Any sources on the net?

Really, if I could learn # theory, I would be set as this is really the only thing I become confused on. I am a liberal arts, non math background. 

I am confused..

For 2^5, you add "1+1" and then come up with 2^6
Then you do the same thing on the bottom except you add "3" but still only increase the exponent by 1 power

How does that work?:(

ps_dahiya · Answer

Remember few simple rules:

1. a^b * a^c = a ^(b+c)

2. a^c * b^c = (a*b)^c

3. 1/(a^b) = a^(-b)

Now lets come to teh question
2^5 + 2^5 = (2^ 5) * (1+1) = 2^5 * 2^1 = 2^(5+1) = 2^6 - Rule 1 above

3^5 + 3^5 + 3^5 = (3^5) * (1+1+1) = 3^5 * 3^1 = 3^(5+1) = 3^6 - Rule 1 above.

Hope this helps.

jamesrwright3 · Answer

I think I am getting it...
Quick question, how would the answer differ, say for instance ,if there were only 2 "3^5" ?

ps_dahiya · Answer

Then answer would be 
2^6 + 2* 3^5
OR
2 * (2^5 + 2^6)

I got this one right but how do I do it without multiplying

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