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, we need to calculate \( 7^3 \):
\[ 7^3 = 7 \times 7 \times 7 \]
Calculating this step-by-step:
- First, calculate \( 7 \times 7 = 49 \).
- Then, multiply that result by 7: \( 49 \times 7 = 343 \).
Therefore, \( 7^3 = 343 \).
Substituting back, we find:
\[ 7^{-3} = \frac{1}{7^3} = \frac{1}{343} \]
Thus, the final answer is:
\[ \frac{1}{343} \]
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