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which of the following is equal to the value of

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papa.baffour
 Post subject: which of the following is equal to the value of
 Post Posted: Thu Aug 13, 2009 2:05 am 
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Course Students


Posts: 7
1. which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5?

a. 5^6
b. 13^5
c. 2^6 + 3^6
d. 2^7 + 3^8
e. 4^5 + 9^5

I'm having issues figuring out how to combine these exponents since it says in the number properties guide that exponents can not be combined when they're being added. Please help.
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furtadovinod
 Post subject: Re: which of the following is equal to the value of
 Post Posted: Thu Aug 13, 2009 10:36 am 
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Students


Posts: 28
papa.baffour wrote:
1. which of the following is equal to the value of 2^5 + 2^5 + 3^5 + 3^5 + 3^5?

a. 5^6
b. 13^5
c. 2^6 + 3^6
d. 2^7 + 3^8
e. 4^5 + 9^5

I'm having issues figuring out how to combine these exponents since it says in the number properties guide that exponents can not be combined when they're being added. Please help.


2^5 + 2^5 can be simplified as 2(2^5).
Similarly, 3^5 + 3^5 + 3^5 can be simplified as 3(3^5).

Now, 2 * (2^5) is nothing but 2^6. Same goes for 3 * (3^5) is 3 ^ 6.

Therefore, the ans is C 2^6 + 3^6.
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papa.baffour
 Post subject: Re: which of the following is equal to the value of
 Post Posted: Thu Aug 13, 2009 10:48 am 
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Course Students


Posts: 7
Thanks for the response. So, just to be clear, you're also saying 4^3 + 4^3 4^3 + 4^3 can be simplified to 4 * (4^3) = 4^4 right?

O.k, so then, what would 4^5 + 4^5 + 4^5 be? Or is can that NOT be simplified further?

Thanks again for your help.
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Ben Ku
 Post subject: Re: which of the following is equal to the value of
 Post Posted: Wed Aug 19, 2009 12:45 pm 
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ManhattanGMAT Staff


Posts: 823
furtadovinod, Good response to the question. It's correct.

Questions such as this one are easier when you are solid on the rules of exponents.

Papa:

Quote:
Thanks for the response. So, just to be clear, you're also saying 4^3 + 4^3 4^3 + 4^3 can be simplified to 4 * (4^3) = 4^4 right?

This is correct.

Quote:
O.k, so then, what would 4^5 + 4^5 + 4^5 be? Or is can that NOT be simplified further?


You can simplify it to 3 * (4^5). Just remember that simplification is only as good as the form you want to simplify it to. For example, the answer choices can have either 4^5 + 4^5 + 4^5 or 3 * (4^5), so you should be comfortable with either expression.

_________________
Ben Ku
Instructor
ManhattanGMAT
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