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# 2^64)^(2^64) = 2^P What does P equal to? This looks

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2^64)^(2^64) = 2^P What does P equal to? This looks [#permalink]  17 Feb 2006, 21:45
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(2^64)^(2^64) = 2^P
What does P equal to?

This looks like a really simple problem. Too bad I remember absolutely nothing from my math days...I do remember a rule that lets you move the power to the front of the equation? Or am I mistaken on that?
Can anyone refresh that concept with me if I remembered it correctly?

Thanks!

P.S. By the way, I don't have the OA...
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Taking the GMAT in five days. CRAM TIME! Should have started preparing sooner

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lol, oops I plugged in some numbers and finally figured it out. The rule was that you could multiply the first power with the base of the second power, in this case you could multiply the first 64 with the second (2^64) on the left side of the equation.....
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Re: PS - two to the powers of... [#permalink]  18 Feb 2006, 06:42
cattalk wrote:
(2^64)^(2^64) = 2^P, What does P equal to?

This looks like a really simple problem. Too bad I remember absolutely nothing from my math days...I do remember a rule that lets you move the power to the front of the equation? Or am I mistaken on that?
Can anyone refresh that concept with me if I remembered it correctly?

Thanks! P.S. By the way, I don't have the OA...

(2^3)^(2^3) = 2^P
(2x2x2)^(2x2x2) = 2^P
(2)^(2x2x2) x (2)^(2x2x2) x (2)^(2x2x2) = 2^P
(2)^(8) x (2)^(8) x (2)^(8) = 2^P
(2)^(8+8+8) = 2^P
(2)^(24) = 2^P

therefore, p = 24 = 3 (2^3)

similarly (2^64)^(2^64) = 2^P
p = 64 x (2^64). i will check, if any.
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(x^y)^z= x^(y*z)

Hence:
(2^64)^(2^64)
=2^(64*(2^64))
=2^((2^6)*(2^64))
=2^(2^(6+64))
=2^(2^70)

P=2^70
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