Question

apply the zero power rule to create an equivalent expression to 9 x (-33) exponent 0 +3/2(8-27 exponent 0)

Answer 1

To simplify the expression \( 9 \cdot (-33)^0 + \frac{3}{2}(8 - 27^0) \), we will use the zero power rule, which states that any non-zero number raised to the power of 0 equals 1.

1. Start by simplifying the terms with exponent 0:
- \((-33)^0 = 1\)
- \(27^0 = 1\)

Now we can rewrite the expression:

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

2. Simplifying further:
- From the first term: \(9 \cdot 1 = 9\)
- For the second part, calculate \(8 - 1 = 7\).

Now substitute this back into the expression:

\[
9 + \frac{3}{2} \cdot 7
\]

3. Next, calculate \(\frac{3}{2} \cdot 7\):
- \(\frac{3}{2} \cdot 7 = \frac{21}{2}\)

4. Now add \(9\) to \(\frac{21}{2}\). To do this, convert \(9\) to have a common denominator:

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

Thus, the expression now becomes:

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

Therefore, the equivalent expression is:

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