Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)to the power of 0+3/2(8−27 to the power of 0)

Question

9
⋅
(
−
33
)
0
+
3
2
(
8
−
27
0
)
.(2 points)

Answer 1

The Zero Power Rule states that any non-zero number raised to the power of 0 is equal to 1.

Let's apply this rule to the expression \( 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) \).

1. First, calculate \((-33)^0\): \[ (-33)^0 = 1 \] Therefore, \( 9 \cdot (-33)^0 = 9 \cdot 1 = 9 \).

2. Next, calculate \(27^0\): \[ 27^0 = 1 \] So, we have \( 8 - 27^0 = 8 - 1 = 7 \).

3. Now calculate \(\frac{3}{2}(7)\): \[ \frac{3}{2} \cdot 7 = \frac{21}{2} \]

4. Finally, combine both parts: \[ 9 + \frac{21}{2} \]

To add these, convert \(9\) into a fraction: \[ 9 = \frac{18}{2} \]

Now add them together: \[ \frac{18}{2} + \frac{21}{2} = \frac{18 + 21}{2} = \frac{39}{2} \]

Thus, the equivalent expression is \[ \frac{39}{2} \]