Question

apply the zero power rule to create an equivalent expression to
(-40)^0 + 1/2(11 - 32^0) = _ + 1/2(_-_)
Fill in the blanks

Answer 1

The zero power rule states that any non-zero number raised to the power of zero equals one. That is, \( a^0 = 1 \) for any \( a \neq 0 \).

Now, let's apply this rule to the expression you provided:

1. The term \( (-40)^0 \) becomes 1 because any non-zero number raised to the power of zero is 1.
2. The term \( 32^0 \) also becomes 1 for the same reason.

Now substitute these values into the expression:

\[
(-40)^0 + \frac{1}{2}(11 - 32^0) = 1 + \frac{1}{2}(11 - 1)
\]

This simplifies to:

\[
1 + \frac{1}{2}(11 - 1) = 1 + \frac{1}{2}(10)
\]

Now calculate \( \frac{1}{2}(10) \):

\[
\frac{1}{2}(10) = 5
\]

So the entire expression simplifies to:

\[
1 + 5 = 6
\]

Filling in the blanks, you have:

\[
(-40)^0 + \frac{1}{2}(11 - 32^0) = 1 + \frac{1}{2}(11 - 1)
\]

Thus, the completed expression is:

\[
1 + 1/2(10)
\]

So the filled blanks would be:

- First blank: 1
- Second blank: 11
- Third blank: 1

The final expression looks like:

\[
1 + \frac{1}{2}(11 - 1)
\]