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:

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