-0.202
Explanation:The given expression is:
[tex]\lbrack(20+21^2-116874\div9)\div(20\div0.09507\times12-21\div(116874\div9))\rbrack^{-1}[/tex]Using the PEMDAS rule, the expression can first be simplified as:
[tex]\lbrack(20+441-12986)\div(\frac{240}{0.09507}-21\div12986)\rbrack^{-1}[/tex][tex]\lbrack-12525\div(2524.456-0.00162)\rbrack^{-1}[/tex]This can be further simplified as:
[tex]\begin{gathered} \lbrack-12525\div2524.454\rbrack^{-1} \\ \lbrack-4.96\rbrack^{-1} \\ -\frac{1}{4.96} \\ =-0.202 \end{gathered}[/tex]