Question

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

+32
(
–
)

Answer 1

To apply the Zero Power Rule, we need to recall that any non-zero number raised to the power of zero is equal to one. Therefore, for any \( a \neq 0 \), we have:

\[ a^0 = 1 \]

Applying this rule to the expression \( 9 \cdot (-33)^0 + 32(8 - 27^0) \):

1. Calculate \( (-33)^0 \):
\[
(-33)^0 = 1
\]

2. Calculate \( 27^0 \):
\[
27^0 = 1
\]

Now substitute these results back into the original expression:

\[
9 \cdot 1 + 32(8 - 1)
\]

This simplifies to:

\[
9 + 32(8 - 1)
\]

Now simplify further:

\[
8 - 1 = 7
\]

So the expression becomes:

\[
9 + 32 \cdot 7
\]

If we calculate \( 32 \cdot 7 \):

\[
32 \cdot 7 = 224
\]

Finally, add \( 9 \) and \( 224 \):

\[
9 + 224 = 233
\]

Thus, the final simplified expression is:

\[
233
\]

Therefore, if we present the equivalent parts of the original expression, we can write:

\[
9 \cdot (-33)^0 + 32(8 - 27^0) = 9 \cdot 1 + 32(8 - 1)
\]

Which is:

\[
= 9 + 32(7)
\]

So your complete equivalent expression with the evaluated components is:

9 ⋅ 1 + 32 (8 - 1) = 9 + 32 (7)