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Exponent

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Director
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Exponent [#permalink]

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New post 19 May 2011, 01:26
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Re: Exponent [#permalink]

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New post 19 May 2011, 06:01
2^{30} = 2^{10} * 2^{10} * 2^{10)

2^{10} = 1024

hence last two digits of 1024 * 1024 * 1024 =

Rof [1024 * 1024 * 1024 ] / 100 = Rof[512 * 1024 * 1024]/ 50

= Rof[12 * 24 * 24 ] / 50 = Rof[6 * 24 * 24] / 25

= Rof [ 6 * (-1) * (-1)] /25 = 6 Hence for last two digits 25 * 4 = 100 means 6 * 4 = 24.

Thus 24 is the last two digits for 1024 * 1024 * 1024.

Now in expression 1024 ^ {3} * 1024 ^ {3} * 1024 ^{3} * 1024 ^{3} we need to find the last two digits.

Hence, 24 * 24 * 24 * 24 will give the last two digits of the expression.

Rof[ 24 * 24 * 24 * 24 ]/ 100 = Rof [ 6 * 24 * 24 * 24] /25 = Rof [ 6 * (-1) * (-1) * (-1) ] / 25 = -6/25

thus remainder is 25-6 = 19.

hence last two digits will be 25 * 4 means 19* 4 = 76.

Thus look for an answer option having last two digits 76.
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Re: Exponent [#permalink]

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New post 19 May 2011, 06:44
What is the question ?
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Director
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Re: Exponent [#permalink]

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New post 19 May 2011, 08:14
hussi9 wrote:
What is the question ?

2^30*2^30*2^30*2^30=2^?
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Re: Exponent [#permalink]

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New post 19 May 2011, 18:16
2^120 or as amit2k9 explained
Re: Exponent   [#permalink] 19 May 2011, 18:16
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