Question

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

Answer 1

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

\[
(-33)^0 = 1 \quad \text{and} \quad 27^0 = 1
\]

Now let's simplify the expression step by step:

1. Substitute the zero power results into the expression:

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

2. Simplify further:

\[
9 + \frac{3}{2}(8 - 1)
\]
This simplifies to

\[
9 + \frac{3}{2} \cdot 7
\]

3. Calculate \(\frac{3}{2} \cdot 7\):

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

4. Combine the two parts:

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

To add these, we should express \(9\) as a fraction with a denominator of \(2\):

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

Thus, we can write:

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

So, the final simplified expression is:

\[
\frac{39}{2}
\]

Therefore, the equivalent expression is

\[
\frac{39}{2}.
\]