To simplify \( 81^{-1/2} \), we can follow these steps:
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First, recognize that \( 81 \) can be rewritten as a power of \( 9 \): \[ 81 = 9^2 \]
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Now substitute \( 81 \) in the expression: \[ 81^{-1/2} = (9^2)^{-1/2} \]
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Apply the power of a power rule (multiply the exponents): \[ (9^2)^{-1/2} = 9^{2 \cdot (-1/2)} = 9^{-1} \]
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Now, rewrite \( 9^{-1} \): \[ 9^{-1} = \frac{1}{9} \]
Therefore, \( 81^{-1/2} = \frac{1}{9} \).
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