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

Answer 1

To simplify the expression \( 9 \times (-33)^0 + \frac{3}{2}(8 - 27^0) \) using the zero power rule, we need to remember that any non-zero number raised to the power of 0 is equal to 1.

1. Simplifying \((-33)^0\): \[ (-33)^0 = 1 \]

2. Simplifying \(27^0\): \[ 27^0 = 1 \]

Now we can substitute these results back into the original expression:

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

This simplifies to:

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

Now, calculate \(\frac{3}{2}(7)\):

\[ \frac{3}{2}(7) = \frac{21}{2} \]

The expression now is:

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

To add these, convert 9 to a fraction with a denominator of 2:

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

So now we can add the two fractions:

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

Thus, the simplified equivalent expression is:

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

Answer 2

whats an equivalent expression to this question?

Answer 3

To create an equivalent expression to the original expression \(9 \times (-33)^0 + \frac{3}{2}(8 - 27^0)\) using the zero power rule, let's reiterate the simplification step but present it more clearly.

1. Applying the zero power rule:

   • \((-33)^0 = 1\)
   • \(27^0 = 1\)

2. Rewrite the expression: \[ 9 \times (-33)^0 + \frac{3}{2}(8 - 27^0) = 9 \times 1 + \frac{3}{2}(8 - 1) \]

3. Simplifying further:

   • This simplifies to: \[ 9 + \frac{3}{2}(7) \]

4. Calculating \(\frac{3}{2}(7)\): \[ \frac{3 \times 7}{2} = \frac{21}{2} \]

5. Adding the results:

   • Convert 9 to a fraction: \[ 9 = \frac{18}{2} \]
   • Now add: \[ \frac{18}{2} + \frac{21}{2} = \frac{39}{2} \]

Equivalent Expression:

Thus, an equivalent expression to the original problem is:

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

This expression is fully simplified and equivalent to the original expression you provided.