Question

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

+32
(
–
)

Answer 1

To apply the Zero Power Rule, we first need to recognize that any non-zero number raised to the power of 0 equals 1. Thus, we can simplify the expression given in the problem:

1. **Starting Expression:**
\( 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) \)

2. **Applying the Zero Power Rule:**
- \( (-33)^0 = 1 \)
- \( 27^0 = 1 \)

Now we substitute these values into the expression:

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

3. **Simplifying Further:**
- The first term simplifies to \( 9 \).
- The second term becomes \( \frac{3}{2}(7) \) since \( 8 - 1 = 7 \).

Calculating \( \frac{3}{2} \cdot 7 \):

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

4. **Final Simplified Expression:**
Thus, the entire expression simplifies to:

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

To express this as a single fraction, we can convert \( 9 \) into a fraction with a denominator of \( 2 \):

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

So now we can add:

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

5. **Conclusion:**
So the equivalent expression for \( 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) \) is:

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

Thus, the answer is:

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