Question

Apply the zero power rule to create an equivalent expression to (-33) to the power of zero + 3/2 (8 minus 27 to the power of 0

Answer 1

The zero power rule states that any non-zero number raised to the power of zero equals one. Therefore, we can simplify the expression given:

1. \((-33)^0 = 1\) (since \(-33\) is non-zero)
2. \(27^0 = 1\) (since 27 is also non-zero)

Now we can substitute these values into the expression:

\[
(-33)^0 + \frac{3}{2} (8 - 27^0) = 1 + \frac{3}{2} (8 - 1)
\]

Next, simplify inside the parentheses:

\[
8 - 1 = 7
\]

Now substitute that back into the expression:

\[
1 + \frac{3}{2} \times 7 = 1 + \frac{21}{2}
\]

Now, we need to combine the terms:

To add 1 to \(\frac{21}{2}\), we can express 1 as \(\frac{2}{2}\):

\[
1 = \frac{2}{2}
\]

So now we can add:

\[
\frac{2}{2} + \frac{21}{2} = \frac{2 + 21}{2} = \frac{23}{2}
\]

Thus, the equivalent expression is:

\[
\frac{23}{2}
\]