Simple

Algebra Level 2

[ 1 65536 ( 1 65536 ) ] [ 1 65536 ( 1 ) 65536 ] = ? \large \left[ { 1 }^{ 65536 }-\left( -{ 1 }^{ 65536 } \right) \right] -\left[ { 1 }^{ 65536 }-\left( -1 \right) ^{ 65536 } \right] = \, ?


The answer is 2.

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2 solutions

Michael Fuller
Feb 14, 2016

[ 1 65536 ( 1 65536 ) ] [ 1 65536 ( 1 ) 65536 ] \left[ { 1 }^{ 65536 }-\left( -{ 1 }^{ 65536 } \right) \right] -\left[ { 1 }^{ 65536 }-\left( -1 \right) ^{ 65536 } \right]

= [ 1 ( 1 ) ] [ 1 ( 1 ) ] = \left[ 1-\left( -1 \right) \right] -\left[ 1-\left( 1 \right) \right]

= [ 2 ] [ 0 ] = \left[ 2 \right] -\left[ 0 \right]

= 2 =\large\color{#20A900}{\boxed{2}}

(-1^65536)=1

Kapil Chandak - 5 years, 3 months ago

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The brackets are not around the -1, so 1 65536 = ( 1 65536 ) = 1 -1^{65536}=-(1^{65536})=-1 .

Michael Fuller - 5 years, 3 months ago

Great fuller

Arun Garg - 5 years, 2 months ago
. .
May 9, 2021

[ 1 65536 ( 1 65536 ) ] [ 1 65536 ( 1 ) 65536 ] = 2 0 = 2 \displaystyle \left [ 1 ^ { 65536 } - \left ( -1 ^ { 65536 } \right ) \right ] - \left [ 1 ^ { 65536 } - \left ( -1 \right ) ^ { 65536 } \right ] = 2 - 0 = \boxed { \color{#D61F06} 2 } .

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