To find the value of \( 4^{-3} \), we can interpret the negative exponent. The expression \( 4^{-3} \) can be rewritten as:
\[ 4^{-3} = \frac{1}{4^3} \]
Now, calculating \( 4^3 \):
\[ 4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64 \]
So,
\[ 4^{-3} = \frac{1}{4^3} = \frac{1}{64} \]
Therefore, the value of \( 4^{-3} \) is
\[ \frac{1}{64} \]
Which corresponds to the response:
\[ \text{1 over 64} \]