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​Find the value of [{(2)2}2]2[\lbrace(2)^2\rbrace^2]^2[{(2)2}2]2​​
Question

Find the value of [{(2)2}2]2[\lbrace(2)^2\rbrace^2]^2

A.

242^4​​

B.

216\tag*{} 2^{16}​​

C.

282^8 ​​

D.

232\tag*{} 2^{32}

Correct option is C

Given:

[{(2)2}2]2[\lbrace(2)^2\rbrace^2]^2

Formula used:

(an)m=anm(a^n)^m=a^{nm} 

Solution:

[{(2)2}2]2[\lbrace(2)^2\rbrace^2]^2 

=[{22×2}]2=[\lbrace2^{2\times 2}\rbrace]^2 

=[24]2=[2^4]^2 

=28=2^8 

​ 


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