To solve \( 7^{-3} \) using the property of negative integer exponents, we can use the rule that states:
\[ a^{-n} = \frac{1}{a^n} \]
Applying this to \( 7^{-3} \):
\[ 7^{-3} = \frac{1}{7^3} \]
Now, calculate \( 7^3 \):
\[ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343 \]
Therefore:
\[ 7^{-3} = \frac{1}{343} \]
The final answer is:
\[ \frac{1}{343} \]