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(_ −_)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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)