According to the Zero Power Rule, any nonzero number raised to the power of 0 equals 1. Therefore, we can simplify the expression \( 1^0 \) as follows:
\[ 1^0 = 1 \]
Now applying this to the expression \( 43(-2 + 1^0) \):
\[ 43(-2 + 1) = 43(-2 + 1) \]
Next, we'll simplify \( -2 + 1 \):
\[ -2 + 1 = -1 \]
So the expression becomes:
\[ 43(-1) \]
Thus, we can write the equivalent expression as:
\[ \frac{4}{3}(-2 + 1^0) = \frac{4}{3}(-2 + 1) \]
So you would fill in the blank with \( 1 \):
\[ \frac{4}{3}(-2 + (1)) \]