The Zero Power Rule states that any non-zero number raised to the power of 0 equals 1. Therefore:
\[ (-40)^0 = 1 \] and \[ 32^0 = 1 \]
Now, substituting these values into the original expression:
\[ (-40)^0 + \frac{1}{2}(11 - 32^0) = 1 + \frac{1}{2}(11 - 1) \]
Now, simplifying inside the parentheses:
\[ 11 - 1 = 10 \]
So, we have:
\[ 1 + \frac{1}{2}(10) \]
Now, calculating \(\frac{1}{2}(10)\):
\[ \frac{1}{2} \times 10 = 5 \]
Now we can write the expression:
\[ 1 + 5 \]
Rearranging this according to your format gives:
\[ (-40)^0 + \frac{1}{2}(11 - 32^0) = 1 + \frac{1}{2}(11 - 1) = 1 + \frac{1}{2}(10) = 1 + 5 \]
Thus, the equivalent expression is:
\[ 1 + \frac{1}{2}(10) \]
So, filling in the blanks, we have:
\[ 1 + \frac{1}{2}(11 - 1) \]
Thus the final answer is:
\[ 1 + \frac{1}{2}(11 - 1) \]
So your completion for the expression format would be:
(−40)^0 + 1/2(11−32^0) = 1 + 1/2(11 − 1)