Let's simplify the following expression:
[tex](2^3)^{-2}[/tex]Step 1:
[tex]\mathrm{Apply\: exponent\: rule}\colon\quad \mleft(a^b\mright)^c=a^{bc},\: \quad \: a\ge0[/tex][tex]\mleft(2^3\mright)^{-2}=2^{3\mleft(-2\mright)}[/tex][tex]=2^{\mleft\{-6\mright\}}[/tex]Step 2:
[tex]\mathrm{Apply\: exponent\: rule}\colon\quad \: a^{-b}=\frac{1}{a^b}[/tex][tex]2^{-6}=\frac{1}{2^6}[/tex][tex]=\frac{1}{64}[/tex]Therefore, the answer is 1/64
