To simplify the expression \(\left(a^{-7}\cdot b^{-2}\right)^{-9}\), we can use the property of exponents that states \((x^m)^n = x^{m \cdot n}\).
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Start with the expression: \[ \left(a^{-7}\cdot b^{-2}\right)^{-9} \]
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Apply the negative exponent: \[ a^{-7 \cdot (-9)} \cdot b^{-2 \cdot (-9)} \]
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This simplifies to: \[ a^{63} \cdot b^{18} \]
Thus, the equivalent expression is: \[ a^{63} \cdot b^{18} \]
From the provided options, the correct choice is:
B) \(a^{63} \cdot b^{18}\).