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
(

)

1 answer

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)