To simplify \( 13^{-6} \cdot 13 \cdot 13^{-3} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
First, rewrite \( 13 \) as \( 13^1 \). Then we have:
\[ 13^{-6} \cdot 13^1 \cdot 13^{-3} = 13^{-6} \cdot 13^1 \cdot 13^{-3} = 13^{-6 + 1 - 3} = 13^{-8} \]
To write the answer in exponential form with positive exponents, we use the property that \( a^{-n} = \frac{1}{a^n} \):
\[ 13^{-8} = \frac{1}{13^8} \]
Thus, the fully simplified form is:
\[ \boxed{\frac{1}{13^8}} \]
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