To simplify \( 243^{3/5} \), we can follow these steps:
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Write 243 as a power of a base: \[ 243 = 3^5 \]
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Substitute this into the expression: \[ 243^{3/5} = (3^5)^{3/5} \]
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Use the power of a power property (multiply the exponents): \[ (3^5)^{3/5} = 3^{(5 \cdot \frac{3}{5})} = 3^3 \]
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Calculate \( 3^3 \): \[ 3^3 = 27 \]
Therefore, the correct simplification of \( 243^{3/5} \) is \( 27 \).