To apply the Zero Power Rule, we need to remember that any non-zero number raised to the power of 0 equals 1.
Thus, \(1^0 = 1\).
Now, substituting this into the expression \( \frac{4}{3}(-2 + 1^0) \):
\[ \frac{4}{3}(-2 + 1) = \frac{4}{3}(-2 + 1) \]
So, \( \frac{4}{3}(-2 + 1^0) \) becomes \( \frac{4}{3}(-2 + 1) \).
To fill in the blank in your question, the equivalent expression \( \frac{4}{3}(-2 + 1^0) \) is:
\[ \frac{4}{3}(-2 + 1) \]
Therefore, the blank should be filled with 1.