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19 May 2011, 02:26
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2^30*2^30*2^30*2^30=?
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19 May 2011, 07:01
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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.
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.
