To solve for \( \log_2 \left( \frac{8^{4/3}}{1} \right) \), we can first simplify the expression inside the logarithm.
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Rewrite \( 8 \) as \( 2^3 \): \[ 8^{4/3} = (2^3)^{4/3} \]
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Use the power of a power property of exponents: \[ (2^3)^{4/3} = 2^{3 \cdot \frac{4}{3}} = 2^4 \]
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Now, we can find \( \log_2(2^4) \): \[ \log_2(2^4) = 4 \]
Thus, \( \log_2 \left( \frac{8^{4/3}}{1} \right) = 4 \).
The answer is \( \boxed{4} \).
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