Apply the Zero Power Rule to create an equivalent expression to

(−40)^0 + 1/2(11−32^0)

(2 points)
(−40)^0 + 1/2(11−32^0) = _+1/2(_ −_)

1 answer

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)