To apply the property of negative integer exponents, we have:
\[ a^{-n} = \frac{1}{a^n} \]
For \( 7^{-3} \), this means:
\[ 7^{-3} = \frac{1}{7^3} \]
Now, we can calculate \( 7^3 \):
\[ 7^3 = 7 \times 7 \times 7 = 343 \]
Thus, substituting back, we get:
\[ 7^{-3} = \frac{1}{343} \]
So the final answer is:
\[ 7^{-3} = \frac{1}{343} \]