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Answer :

Given the indices below,

[tex](-2^3)^{-2}[/tex]

Simplifying the indices by converting it to positive indices,

[tex](-2^3)^{-2}=(-2\times-2\times-2)^{-2}=(-8)^{-2}=(\frac{-1}{8})^2=(\frac{-1}{8}\times\frac{-1}{8})=\frac{1}{64}[/tex]

Since the value 1/64 is greater than 0 but less than 1,

Hence, the value of the expression lies between 0 and 1.