Apply the Zero Power Rule to create an equivalent expression to 9*(-33)⁰+ 3/2(8-27⁰). (2 points)

Question

9*(-33)⁰+ 3/2(8-27⁰) =blank*blank + 3/2(blank-blank)

Answer 1

To apply the Zero Power Rule, we need to acknowledge that any non-zero number raised to the power of zero is equal to 1. Therefore:

1. For the term \((-33)^0\): \((-33)^0 = 1\)

2. For the term \(27^0\): \(27^0 = 1\)

Now substituting these values into the expression \(9*(-33)^0 + \frac{3}{2}(8 - 27^0)\):

1. Substitute \((-33)^0\) with \(1\): \[ 9*(-33)^0 = 9*1 = 9 \]

2. Substitute \(27^0\) with \(1\): \[ 8 - 27^0 = 8 - 1 = 7 \]

Now, we can simplify the entire expression: \[ 9*(-33)^0 + \frac{3}{2}(8 - 27^0) = 9 + \frac{3}{2}(7) \]

Now, let's express it in the requested format: \[ 9 \cdot 1 + \frac{3}{2} \cdot (8 - 1) \Rightarrow 9 \cdot 1 + \frac{3}{2} \cdot 7 \]

Thus, the expression can be represented as: \[ 9*(1) + \frac{3}{2}(8-1) \]

So, filling in the blanks: \[ \boxed{9*1 + \frac{3}{2}(8-1)} \]