To simplify the expression \((8 r^{-5})^{-3}\), you can apply the property of exponents that states \((a^m)^n = a^{m \cdot n}\).
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Apply the exponent to each part: \[ (8 r^{-5})^{-3} = 8^{-3} \cdot (r^{-5})^{-3} \]
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Simplify each part: \[ 8^{-3} = \frac{1}{8^3} = \frac{1}{512} \] and \[ (r^{-5})^{-3} = r^{(-5) \cdot (-3)} = r^{15} \]
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Combine the results: \[ (8 r^{-5})^{-3} = \frac{1}{512} \cdot r^{15} = \frac{r^{15}}{512} \]
Thus, the simplified form of the expression \((8 r^{-5})^{-3}\) is:
\[ \frac{r^{15}}{512} \]
The correct answer is:
\(\frac{r^{15}}{512}\)