To apply the Zero Power Rule to the expression \( \frac{4}{3}(-2 + 1^0) \), we need to evaluate \( 1^0 \).
According to the Zero Power Rule, any non-zero number raised to the power of zero equals 1. Therefore:
\[ 1^0 = 1. \]
Now substituting \( 1^0 \) back into the expression:
\[ \frac{4}{3}(-2 + 1) = \frac{4}{3}(-2 + 1). \]
Now we can simplify:
\[ -2 + 1 = -1. \]
Thus, the expression can be simplified to:
\[ \frac{4}{3}(-1). \]
Therefore, an equivalent expression to \( \frac{4}{3}(-2 + 1^0) \) is:
\[ -\frac{4}{3}. \]
In simplified form without the numerical constant, it shows that the answer can still be interpreted as:
\[ \frac{4}{3}(-2 + 1^0) = \frac{4}{3}(-2 + 1) = \frac{4}{3}(-1). \]
So, an equivalent expression focusing on the initial query might also state:
\[ \frac{4}{3}(-2 + \textbf{1}). \]