Simple

Algebra Level 1

( ( ( 2 2 ) 2 ) 2 ) 2 = ? \Large (((2^2)^2)^2)^2 = \, ?

81832 65536 53472 86266

Felix Lu by Felix Lu , 18, USA

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5 solutions

Ashish Menon
Jun 1, 2016

The answer is 2 16 = 65536 2^{16} = \color{#69047E}{\boxed{65536}} .

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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. . - 3 months, 4 weeks ago
Ananth Jayadev
Jan 15, 2016

Simply multiply all of the exponents in the expression to get 2 16 = 65536 2^{16} = 65536 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused
. .
Feb 17, 2021

( ( ( 2 2 ) 2 ) 2 ) 2 = ( ( ( 4 ) 2 ) 2 ) 2 = ( ( 16 ) 2 ) 2 = ( 256 ) 2 = 65536 ( ( ( 2 ^ { 2 } ) ^ { 2 } ) ^ { 2 } ) ^ { 2 } = ( ( ( 4 ) ^ { 2 } ) ^ { 2 } ) ^ { 2 } = ( ( 16 ) ^ { 2 } ) ^ { 2 } = ( 256 ) ^ { 2 } = 65536 .

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Lew Sterling Jr
May 21, 2019

( ( ( 2 2 ) 2 ) 2 ) 2 Method 1: Method 2: = ( ( ( 4 ) 2 ) 2 ) 2 = ( ( 2 2 ) 2 ) 4 = ( ( 16 ) 2 ) 2 = ( 2 2 ) 8 = ( 256 ) 2 = 2 16 = 65536 = 65536 \begin{matrix} &\left(\left(\left(2^2\right)^2\right)^2\right)^2&\\ \textrm{Method 1:}&&\textrm{Method 2:}\\ =\left(\left(\left(4\right)^2\right)^2\right)^2&&=\left(\left(2^2\right)^2\right)^4\\ =\left(\left(16\right)^2\right)^2&&=\left(2^2\right)^8\\ =\left(256\right)^2&&=2^{16}\\ =\textbf{65536}&&=\textbf{65536}\\ \end{matrix}

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Galen Buhain
Nov 25, 2016

(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2)(2) = 65536

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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