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Exponents

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flash2374
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Exponents [#permalink] New post   Updated on: 02 May 2010, 12:53
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\(\frac{(8^2)(3^3)(2^4)}{96^2} =\)

Can you please solve? What level question is this?



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Originally posted by flash2374 on 02 May 2010, 11:39.
Last edited by flash2374 on 02 May 2010, 12:53, edited 1 time in total.
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Re: Exponents [#permalink] New post   02 May 2010, 12:12
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flash2374 wrote:
\(\frac{(8^2)(3^2)(2^4)}{96^2} =\)

Can you please solve? What level question is this?



Take denominator first = (96^2) = (32*3)^2 = (2^5*3)^2 = 2^10*3^2

Numerator = (8^2)(3^2)(2^4) = 2^6*3^2*2^4 = 2^10*3^2

So answer is \(\frac{2^10*3^2}{2^10*3^2} =\) = 1
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Re: Exponents [#permalink] New post   02 May 2010, 12:56
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flash2374 wrote:
\(\frac{(8^2)(3^3)(2^4)}{96^2} =\)

I'm sorry, I originally mistyped 3^2 instead of 3^3. Can you please solve it again? The answer should come to 3.



Yes, the answer should be 3 in that case ..!
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Re: Exponents [#permalink] New post   03 May 2010, 15:22
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gxsingh wrote:
I personally prefer the way silvers solved it!

Agreed! Prime factoring is the way to go!



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Re: Exponents [#permalink] New post   02 May 2010, 11:58
flash2374 wrote:
\(\frac{(8^2)(3^2)(2^4)}{96^2} =\)

Can you please solve? What level question is this?


I guess this must be around 600-650 types level question not sure though .. !

Anyway you can break down this expression to make it simple

\(\frac{(8^2)(3^2)(2^4)}{96^2} = \frac{(8^ 2) (3^2) (2^4)}{(16 * 6 *16 * 6)}\)

And then u can easily solve this one ..!
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Re: Exponents [#permalink] New post   02 May 2010, 12:52
\(\frac{(8^2)(3^3)(2^4)}{96^2} =\)

I'm sorry, I originally mistyped 3^2 instead of 3^3. Can you please solve it again? The answer should come to 3.
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Re: Exponents [#permalink] New post   02 May 2010, 13:20
Thanks. I see it now.
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Re: Exponents [#permalink] New post   02 May 2010, 13:33
nitishmahajan wrote:
flash2374 wrote:
\(\frac{(8^2)(3^2)(2^4)}{96^2} =\)

Can you please solve? What level question is this?


I guess this must be around 600-650 types level question not sure though .. !

Anyway you can break down this expression to make it simple

\(\frac{(8^2)(3^2)(2^4)}{96^2} = \frac{(8^ 2) (3^2) (2^4)}{(16 * 6 *16 * 6)}\)

And then u can easily solve this one ..!


I solved the answer with Silver's explanation. I'm just curious to understand your reasoning. I see that 16 * 6 is 96 so 96^2 would be 16 * 6 * 16 * 6. Then you can cancel out 2^4 and one of the 16s. You are left with (8^2)(3^3)/(16*6*6). Then you can make it (4 * 27) / 36. Then (4 * 3) / 4 = 3.
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Re: Exponents [#permalink] New post   02 May 2010, 18:31
flash2374 wrote:
nitishmahajan wrote:
flash2374 wrote:
\(\frac{(8^2)(3^2)(2^4)}{96^2} =\)

Can you please solve? What level question is this?


I guess this must be around 600-650 types level question not sure though .. !

Anyway you can break down this expression to make it simple

\(\frac{(8^2)(3^2)(2^4)}{96^2} = \frac{(8^ 2) (3^2) (2^4)}{(16 * 6 *16 * 6)}\)

And then u can easily solve this one ..!


I solved the answer with Silver's explanation. I'm just curious to understand your reasoning. I see that 16 * 6 is 96 so 96^2 would be 16 * 6 * 16 * 6. Then you can cancel out 2^4 and one of the 16s. You are left with (8^2)(3^3)/(16*6*6). Then you can make it (4 * 27) / 36. Then (4 * 3) / 4 = 3.


you can actually solve this with many ways, generally I try to cancel the big numbers, so that the calculation becomes easier later on .. and it also decreases the number steps involved for me ... Anyway, one should follow the method with which they are comfortable with ..!
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Re: Exponents [#permalink] New post   03 May 2010, 11:02
I personally prefer the way silvers solved it!
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Re: Exponents [#permalink] New post   03 May 2010, 11:14
flash2374 wrote:
nitishmahajan wrote:
flash2374 wrote:
\(\frac{(8^2)(3^2)(2^4)}{96^2} =\)

Can you please solve? What level question is this?


I guess this must be around 600-650 types level question not sure though .. !

Anyway you can break down this expression to make it simple

\(\frac{(8^2)(3^2)(2^4)}{96^2} = \frac{(8^ 2) (3^2) (2^4)}{(16 * 6 *16 * 6)}\)

And then u can easily solve this one ..!


I solved the answer with Silver's explanation. I'm just curious to understand your reasoning. I see that 16 * 6 is 96 so 96^2 would be 16 * 6 * 16 * 6. Then you can cancel out 2^4 and one of the 16s. You are left with (8^2)(3^3)/(16*6*6). Then you can make it (4 * 27) / 36. Then (4 * 3) / 4 = 3.


Choose the method that suits u the best and will give u the most confident(hopefully the right) answer in the shortest period of time :-D
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Re: Exponents [#permalink]
03 May 2010, 11:14
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