The complete order of operations for this expression is: (4³×(10-2)³) ÷ 2.
According to the order of operations, the exponentiation operation should be completed first in the given expression 4×10-2 to the third power divided by two.
To determine which operation in the given expression should be completed first according to the order of operations, we need to follow the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
In the expression 4×10-2 to the third power divided by two, the first operation to be completed is the exponentiation, as it is the highest priority operation.
We raise 4×10-2 to the third power, which gives us (4×10-2)³. Next, we perform the multiplication, which gives us (4³×(10-2)³). Finally, we divide the result by two.
Therefore, the complete order of operations for this expression is: (4³×(10-2)³) ÷ 2.