Question

Apply zero power rule to create equivalent expression
(-40)^0 + 1/2 (11-32°)

Answer 1

The zero power rule states that any non-zero number raised to the power of zero is equal to one. Therefore, for \((-40)^0\), we have:

\[
(-40)^0 = 1
\]

Now, substituting this into the expression we have:

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

Next, we can simplify \(\frac{1}{2} (11 - 32^\circ)\):

\[
11 - 32^\circ = 11 - 32 = -21
\]

Now substituting \(-21\) into the expression gives:

\[
\frac{1}{2}(-21) = -\frac{21}{2}
\]

Putting this all together:

\[
1 + \left(-\frac{21}{2}\right) = 1 - \frac{21}{2}
\]

To add these, we need a common denominator. The number \(1\) can be expressed as \(\frac{2}{2}\):

\[
\frac{2}{2} - \frac{21}{2} = \frac{2 - 21}{2} = \frac{-19}{2}
\]

Thus, the equivalent expression is:

\[
\frac{-19}{2}
\]