What will be the value of $(8)^{(3^{- 1})}$ ?

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\frac{8}{3}

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\frac{1}{2}

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Solution

The correct option is C 2
$8^{(3^{- 1})}$ = $(2^{3})^{(3^{- 1})}$ $[∵ 8 = 2^{3}]$

[Applying: $(a^{m})^{n}$ = $a^{n m}$ ]
$(2^{3})^{(3^{- 1})} = 2^{(3 \times \frac{1}{3})} = 2^{1} = 2$

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