Can anyone explain the reasoning behind this? The only way it makes sense to me is when I do the arithmetic to get the answer.
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bradyhopkins
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Can anyone explain the reasoning behind this? The only way it makes sense to me is when I do the arithmetic to get the answer.
Here is how you should approach this problem.
2^5 + 2^5 is really just 2(2^5)...once it is in
this form we know that 2 is just 2^1. So 2^1 * 2^5
means we add the exponents hence 2^6. Same thing for
the 3's...3(3^5) = 3^1 + 3^5 = 3^6.
2^5 + 2^5 is really just 2(2^5)...once it is in
this form we know that 2 is just 2^1. So 2^1 * 2^5
means we add the exponents hence 2^6. Same thing for
the 3's...3(3^5) = 3^1 + 3^5 = 3^6.
Last edited by brood1989 on Tue Apr 19, 2011 9:44 am, edited 2 times in total.
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Brent@GMATPrepNow
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Sometimes it's hard to see that numbers behave the same as variables do.
We know that x + x + y + y + y can be rewritten as 2x + 3y
Similarly, 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2(2^5) + 3(3^5)
From here we can simplify 2(2^5) + 3(3^5) as 2^6 + 3^6
We know that x + x + y + y + y can be rewritten as 2x + 3y
Similarly, 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2(2^5) + 3(3^5)
From here we can simplify 2(2^5) + 3(3^5) as 2^6 + 3^6
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manpsingh87
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well concept involved here is that, when two or more numbers are multiplied whose bases are same, then their powers get added. i.e. x^y*x^2=x^(y+2),bradyhopkins wrote:
Can anyone explain the reasoning behind this? The only way it makes sense to me is when I do the arithmetic to get the answer.
now 2^5+2^5= 2^5(1+1)=2^5*2=2^(5+1);=2^6;
similarly 3^5+3^5+3^5=3^5(1+1+1)=3^5*3=3^6;
hence our answer is 2^6+3^6;
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