Question

Which of the following expressions is equal to 1 divided by 16

Answer 1

The correct answer is:  [A]:  " ($\frac{1}{2}$)⁴ " .
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Note:  ($\frac{1}{2}$)⁴  = $\frac{1^{4} }{2^{4} }$ ;

                                                = $\frac{1*1*1*1}{2*2*2*2}$ ;

                                                = $\frac{1}{16}$ .
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Consider "Choice [B]" :  "($\frac{1}{2}$)⁴ " ;

Note:  ($\frac{1}{4}$)⁴ =  $\frac{1^{4} }{4^{4} }$ ;

                                                = $\frac{1*1*1*1}{4*4*4*4}$ ;

                                                = $\frac{1}{256}$ .

Note that:  "$\frac{1}{256}$" $\neq$ "$\frac{1}{16}$" .
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Consider "Choice [C]" :  "($\frac{1}{8}$)² " ; 

Note:  ($\frac{1}{8}$)²  = $\frac{1^{2} }{8^{2} }$ ;

                                                = $\frac{1*1}{8*8}$ ;

                                                = $\frac{1}{64}$ .

Note that:  "$\frac{1}{64}$" $\neq$ "$\frac{1}{16}$" .
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     →  As such, the only correct answer choice is:
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Answer choice:   [A]:  " ($\frac{1}{2}$)⁴ " .
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