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M06 P.S Q20

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M06 P.S Q20 [#permalink] New post 12 Dec 2009, 11:17
In the attaced question.

I feel answer choice should have been 25^(root2) instead of 25^2(root2)?

Please let me know if my understanding is correct
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CIO
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Re: M06 P.S Q20 [#permalink] New post 17 Dec 2009, 00:02
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Tania, consider these examples:

(5^1)^2 = 5^2 = 25 --> the answer is 5^2, not 25^2, which would equal 5^4 (incorrect).

(5^2)^2 = 5^{2*2} = 5^4 = 625 = 25^2 --> You see that we had to multiply the exponents (2*2) but didn't change the base at that stage yet. If we follow your logic we end up with 25^{2*2}, which is not right since we've squared the expression 5^2 twice, not once (we squared the base and multiplied the exponent by 2).

Let's see our problem again:

(5^{\sqrt{2}})^2 = 5^{2\sqrt{2}} = (5^2)^{\sqrt{2}} = 25^{\sqrt{2}} --> make sure you square the expression once

So, the right answer could be either 25^{\sqrt{2}} or 5^{2\sqrt{2}}. I hope it helped make it a bit clearer.
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Re: M06 P.S Q20 [#permalink] New post 15 Dec 2009, 18:34
tania wrote:
In the attaced question.

I feel answer choice should have been 25^(root2) instead of 25^2(root2)?

Please let me know if my understanding is correct


the answer says B 25^root 2

Am I missing something or just an oversight?
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Re: M06 P.S Q20 [#permalink] New post 16 Dec 2009, 03:01
The correct answer is B, not D. B is exactly what you think the right answer should be :).
tania wrote:
In the attaced question.

I feel answer choice should have been 25^(root2) instead of 25^2(root2)?

Please let me know if my understanding is correct

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Re: M06 P.S Q20 [#permalink] New post 16 Dec 2009, 13:28
My bad, I mean to type the choice should have been of 25^2(root2) instead of 25^(root2) .

Can someone please explain the property of exponent for this question?
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Re: M06 P.S Q20 [#permalink] New post 16 Dec 2009, 13:38
tania wrote:
My bad, I mean to type the choice should have been of 25^2(root2) instead of 25^(root2) .

Can someone please explain the property of exponent for this question?


Maybe it would be easier with another number

Lets say 4^sqrt 4
this would = 16

now let's say (4^sqrt4)^2 = 256

remember 5^2 * 5^3 = 5^5 because we add the exponents

so from the above example we would get 4^(2*sqrt 4)
that would in turn = 16 ^ sqrt 4 (if you wanted to solve that would equal 16*16) or 256 same as above

the point is that you add the square root not square the square root and keep the base number the same
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Re: M06 P.S Q20 [#permalink] New post 21 Dec 2009, 14:53
u ppl are awesome...thnx a lot for your explanations.
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Re: M06 P.S Q20 [#permalink] New post 15 Feb 2010, 17:46
Hey Guys, I have one quick question on this one.
By mistake i solved this one as

square of (5 ^ sqrt(2)) = (5 ^ (2 ^ (1/2) )) raised to 2.

1/2 and 2 cancels out leaving 5 ^ 2 = 25.
I am not sure whats wrong in this approach. Can someone please tell me.

Thanks in advance.
Re: M06 P.S Q20   [#permalink] 15 Feb 2010, 17:46
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