2^5 +2 ^5 +3^5 +3^5 +3^5

[GUEST 09.09]

Hi- i got this problem correct and it was a lucky guess. Can someone explain the rules to this and provide an explanation?

2^5 +2 ^5 +3^5 +3^5 +3^5?

Thanks!!

[Khalid]

Since the root is constant, you can simply add the numbers preceeding the root, keeping the root same.
2^5+2^5+3^5+3^5+3^5= 13^5

[StaceyKoprince]

Please post the entire problem if you would like an instructor to apply. Also, Khalid, your calculation is not correct.

Try this:
2^2 + 2^2 = 4 + 4 = 8
but if I followed your calculation, I'd end up with 4^2 = 16. Not the same number.

[gphil]

I don't know whether it is the fastest way, but here is a solution

2^5 +2 ^5 +3^5 +3^5 +3^5 = 2*2^5 + 3*3^5 = 2*32+3*243=64+729=793
or = 2^6+3^6 = 793
It would be great to see the answer chioces.

[RonPurewal]

The last post has the correct answer, but glosses over WHY it's the correct answer. Specifically,
2 * (2^5) is 2 * (2*2*2*2*2), which is 2*2*2*2*2*2 = 2^6.
The same reasoning shows that 3 * (3^5) is 3^6; try this yourself and make sure that you can derive it.

I'm assuming that the answer choices (which you didn't post) were left in exponential form: i.e., the correct answer was in all likelihood written as 2^6 + 3^6. I'd be awfully surprised if the GMAT actually wanted you to calculate the answer.

Incidentally, the numbers in this problem aren't all that big, so you could just multiply the original expression out - 32 + 32 + 243 + 243 + 243 = 793 - and then do the same with the answer choices. It's ugly, but you could probably do it in two minutes if you concentrate really hard (and if you haven't grown up using a calculator since the age of six).

[sabbatini_mileise]

I am not understanding:
2^5+2^5 = 2(2^5)?
How? Likewise, 3^5+3^5+3^5=3(3^5)?

I slept on it, and it came to me in my sleep! I got it!

Just as we would:
x^2+x^2 = 2(x^2)

Thank you!

[ali_sha12j]

The last post has the correct answer, but glosses over WHY it's the correct answer. Specifically,
2 * (2^5) is 2 * (2*2*2*2*2), which is 2*2*2*2*2*2 = 2^6.
The same reasoning shows that 3 * (3^5) is 3^6; try this yourself and make sure that you can derive it.

I'm assuming that the answer choices (which you didn't post) were left in exponential form: i.e., the correct answer was in all likelihood written as 2^6 + 3^6. I'd be awfully surprised if the GMAT actually wanted you to calculate the answer.

Incidentally, the numbers in this problem aren't all that big, so you could just multiply the original expression out - 32 + 32 + 243 + 243 + 243 = 793 - and then do the same with the answer choices. It's ugly, but you could probably do it in two minutes if you concentrate really hard (and if you haven't grown up using a calculator since the age of six).

2^5+2^5=2*2^5. makes sense but i am still not sure why 3^5+3^5+3^5=3*3^5.
why it cant be 3*3*3^5=3^7?

[messi10]

Hi ali_sha12j,

You can try this solution and it may work for you:

I slept on it, and it came to me in my sleep! I got it!

If you are not as lucky as sabbatini, please read on. :)

Forget the powers for a second. Lets say you have this expression:

7 + 7 + 7

Clearly, this is equal to 21. But I will manipulate it a bit and write it as:

7(1 + 1 + 1) = 7 (3) = 21

Basically I just took 7 out as a common factor. Now lets replace 7 with our original expression of 3^5

3^5 + 3^5 + 3^5 = 3^5 (1 + 1 + 1) = 3^5 (3) or 3 x 3^5 = 3^6

Hope this helps.

Regards

Sunil

[ali_sha12j]

thanks!
i got it now :)

[RonPurewal]

thanks!
i got it now :)

great.

in any case, make sure that you don't underestimate the power of simply doing out the arithmetic, as remarked in the last part of this earlier post:
post4996.html#p4996

this is the kind of question that you really shouldn't get wrong, because, even if you don't know how to do the algebra, you can just start firing away on the arithmetic. (obviously, not all problems with exponents are like that, but you should know that it's an option some of the time.)