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:

$$\frac{39}{2}$$