Question

Exponent rules unit test

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

Answer 1

To apply the Zero Power Rule, which states that any number (except zero) raised to the power of zero equals 1, let's simplify the given expression step-by-step:

Original expression:
\[ 9 \cdot (-33)^0 + \frac{3}{2}(8 - 270) \]

1. Apply the Zero Power Rule:
\[ (-33)^0 = 1 \]

So the expression becomes:
\[ 9 \cdot 1 + \frac{3}{2}(8 - 270) \]

2. Simplify \( 9 \cdot 1 \):
\[ 9 \cdot 1 = 9 \]

Now the expression is:
\[ 9 + \frac{3}{2}(8 - 270) \]

3. Simplify inside the parentheses:
\[ 8 - 270 = -262 \]

Now the expression is:
\[ 9 + \frac{3}{2}(-262) \]

4. Multiply \(\frac{3}{2}\) by \(-262\):
\[ \frac{3}{2} \cdot (-262) = \frac{3 \cdot -262}{2} = \frac{-786}{2} = -393 \]

Now the expression is:
\[ 9 + (-393) \]

5. Finally, simplify \( 9 + (-393) \):
\[ 9 - 393 = -384 \]

So, the equivalent expression is:
\[ -384 \]

The filled in boxes are:
\[ 9 \cdot 1 + \frac{3}{2}( -262 ) = -384 \]