Question

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

Answer 1

The Zero Power Rule states that any non-zero number raised to the power of zero is equal to 1, i.e., \( a^0 = 1 \) for any \( a \neq 0 \).

Let's apply this rule step by step to the expression \( 9 \cdot (-33)^0 + 32(8 - 27^0) \):

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

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

3. Now substitute these results back into the expression:
\[
9 + 32(7)
\]

4. Finally, simplify \( 32(7) \):
\[
32(7) = 224
\]

5. Therefore, the final expression becomes:
\[
9 + 224 = 233
\]

Putting everything together, the equivalent expression using the Zero Power Rule is:
\[
9 + 224 = 233
\]

Thus, the simplified and equivalent expression is \( 233 \).