To simplify the expression \( 13^{-6} \times 13 \times 13^{-2} \), we can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).
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First, rewrite the expression with the exponents combined: \[ 13^{-6} \times 13^{1} \times 13^{-2} = 13^{-6 + 1 - 2} \]
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Now, simplify the exponent: \[ -6 + 1 - 2 = -7 \]
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Thus, we have: \[ 13^{-7} \]
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To express the answer in exponential form with positive exponents, we rewrite \( 13^{-7} \) as: \[ \frac{1}{13^7} \]
Therefore, the fully simplified expression is: \[ \frac{1}{13^7} \]
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