To simplify the expression \( 125^{4/3} \), we can break it down into steps:
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First, rewrite \( 125 \) as a power of \( 5 \): \[ 125 = 5^3 \]
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Now substitute \( 125 \) in the expression: \[ 125^{4/3} = (5^3)^{4/3} \]
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Use the power of a power property of exponents, which states that \( (a^m)^n = a^{mn} \): \[ (5^3)^{4/3} = 5^{3 \cdot (4/3)} \]
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Multiply the exponents: \[ 3 \cdot (4/3) = 4 \] So, we have: \[ 5^{4} \]
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Finally, calculate \( 5^4 \): \[ 5^4 = 625 \]
Thus, the simplified form of \( 125^{4/3} \) is: \[ \boxed{625} \]
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