To simplify the expression \( (9^{-2} \times 9^{7})^{-3} \), we can follow these steps:
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Use the property of exponents that states \( a^m \times a^n = a^{m+n} \): \[ 9^{-2} \times 9^{7} = 9^{-2 + 7} = 9^{5} \]
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Now, take this result and raise it to the power of \(-3\): \[ (9^{5})^{-3} = 9^{5 \times -3} = 9^{-15} \]
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Finally, we can express \( 9^{-15} \) as: \[ 9^{-15} = \frac{1}{9^{15}} \]
So the expression \( (9^{-2} \times 9^{7})^{-3} \) simplifies to \( \frac{1}{9^{15}} \).
Thus, the correct equivalent expression is: \[ \frac{1}{9^{15}} \]
Therefore, the answer is: 1 divided by 9 raised to the fifteenth power.