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

Question

fill in the blanks

Answer 1

To apply the Zero Power Rule, we know that any non-zero number raised to the zero power equals 1. Thus, we can simplify the expression as follows:

1. \( (-33)^0 = 1 \)
2. \( 27^0 = 1 \)

Now we simplify the original expression step-by-step:

Given expression:

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

Substituting in the values we found:

\[ 9 \cdot 1 + \frac{3}{2} (8 - 1) \]

This simplifies to:

\[ 9 + \frac{3}{2} (7) \]

Now, we fill in the blanks.

1. The final equivalent expression which maintains the form would be:
   • The first term is: 9
   • The second term in parentheses: 1
   • The third term in parentheses: 8
   • The fourth term: 1

Filling the blanks gives:

9⋅(−33)^0 + 3/2(8−27^0) = 9 ⋅ 1 + 3/2(8 - 1)

So, the final answer is:

9 ⋅ 1 + 3/2(8 - 1)