Answer:
309.91
Step-by-step explanation:
The "work" is best done by a reliable calculator that follows the order of operations. The result of that work is shown in the attachment.
[tex]-0.1+\dfrac{12.4}{(-0.2)^2}+0.01\\\\=-0.1+\dfrac{12.4}{0.04}+0.01\\\\=-0.1+310+0.01\\\\=309.9+0.01=\boxed{309.91}[/tex]
_____
Additional comment
According to the order of operations, exponents are evaluated first, then division, then addition and subtraction (left to right).
Of course, the addition can be done in any order (as long as the sign is kept with the number), since addition is commutative and associative.
The division could be done by multiplying by (10/2) twice, to get ...
12.4/(-0.2)² = 12.4(10/2)(10/2) = (124/2)(10/2) = 62(10/2) = 620/2 = 310
This would be an example of making use of substitution and the properties of multiplication, division, and multiplicative inverse. The Order of Operations seems to ignore these properties.
