To simplify the expression \({ (7^5)(7^3) }^{-4}\), we can follow these steps:
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Simplify inside the braces using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\): \[ 7^5 \cdot 7^3 = 7^{5+3} = 7^8 \]
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Now the expression becomes: \[ (7^8)^{-4} \]
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Next, we apply the power of a power property, which states \((a^m)^n = a^{m \cdot n}\): \[ (7^8)^{-4} = 7^{8 \cdot (-4)} = 7^{-32} \]
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Finally, since \(7^{-32} = \frac{1}{7^{32}}\), we can identify the simplified expression among the provided options: \[ \frac{1}{7^{32}} \]
Thus, the expression simplifies to \( \frac{1}{7^{32}} \).