Question

Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)0+32(8−270) .(2 points) 9⋅(−33)^0+3/2(8−27^0) = blank ⋅ blank +3/2 (blank – blank)

Answer 1

The Zero Power Rule states that any non-zero number raised to the power of zero is equal to 1. Therefore:

1. For \((-33)^0\), we have:
\[
(-33)^0 = 1
\]

2. For \(27^0\), similarly:
\[
27^0 = 1
\]

Now, let's apply this to simplify the original expression:

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

Substituting in the values we've calculated:

\[
9 \cdot 1 + \frac{3}{2}(8 - 1)
\]

This simplifies to:

\[
9 + \frac{3}{2}(7)
\]

Now, calculating \(\frac{3}{2}(7)\):

\[
\frac{3 \cdot 7}{2} = \frac{21}{2}
\]

Putting everything together gives us:

\[
9 + \frac{21}{2}
\]

Now, to express \(9\) in terms of halves, we can write it as:

\[
\frac{18}{2}
\]

Thus we have:

\[
\frac{18}{2} + \frac{21}{2} = \frac{39}{2}
\]

In the format requested, we can break it down in the following way:

\[
9 \cdot (1) + \frac{3}{2}(8 - 1)
\]

Which can be filled in as:

\[
9 \cdot 1 + \frac{3}{2}(8 - 1)
\]

Thus, the equivalent expression with the blanks filled is:

\[
9 \cdot 1 + \frac{3}{2}(8 - 1)
\]

So the filled blanks are:

\[
\text{blank} = 9, \text{blank} = 1, \text{blank} = 8, \text{blank} = 1
\]