To apply the Zero Power Rule, we need to recognize that any non-zero number raised to the power of 0 is equal to 1. In your expression, we have \( 1^0 \).
Calculating \( 1^0 \):
\[ 1^0 = 1 \]
Now, we can substitute \( 1 \) for \( 1^0 \) in the original expression:
\[ -\frac{4}{3}(-2 + 1^0) = -\frac{4}{3}(-2 + 1) \]
Now, simplifying the expression inside the parentheses:
\[ -2 + 1 = -1 \]
So now we have:
\[ -\frac{4}{3}(-1) = \frac{4}{3} \]
Therefore, the equivalent expression to \( \frac{4}{3}(-2 + 1^0) \) is:
\[ \frac{4}{3}(-2 + \underline{1}) \]
Thus, the blank can be filled with \( 1 \).
The equivalent expression, with the zero power applied, is:
\(\frac{4}{3}(-2 + \underline{1})\).