Estimate the value that should replace the question mark (?) in the following expression:

$109.09+511.98÷15.97-?{\mathrm{²}}^{}=\left(20.99\right)2^{}-($\(19.96\) ) 2

The correct option is 10.

To estimate the value that should replace the question mark (?), we can round each decimal number in the expression to its nearest whole number:

$109.09\approx 109$
$511.98\approx 512$
$15.97\approx 16$
$20.99\approx 21$
$19.96\approx 20$

Substituting these rounded values into the original equation gives:

$109+512÷16-{?}^2={21}^2-{20}^2$

Step 1: Simplify the division on the left-hand side (LHS) following BODMAS rules.

$512÷16=32$

Now, simplify the addition on the left-hand side:

$109+32-{?}^2=141-{?}^2$

Step 2: Calculate the right-hand side (RHS).

${21}^2=441$
${20}^2=400$
${21}^2-{20}^2=441-400=41$

Step 3: Equate LHS and RHS to solve for ?.

$141-{?}^2=41$
${?}^2=141-41$
${?}^2=100$
$?=\sqrt{100}=10$

Thus, the estimated value that replaces the question mark is 10.