To determine which expression simplifies to \( 8 \cdot 3^{\sqrt{7}} \), let's simplify each of the given options step by step:
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Negative 6 cube root of 7 minus 2 cube root of 7: \[ -6 \sqrt[3]{7} - 2 \sqrt[3]{7} = (-6 - 2) \sqrt[3]{7} = -8 \sqrt[3]{7} \]
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3 cube root of 6 plus 5 cube root of 1: \[ 3 \sqrt[3]{6} + 5 \sqrt[3]{1} = 3 \sqrt[3]{6} + 5 \cdot 1 = 3 \sqrt[3]{6} + 5 \] This does not resemble \( 8 \cdot 3^{\sqrt{7}} \).
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Cube root of 56 plus 6 cube root of 7: \[ \sqrt[3]{56} + 6 \sqrt[3]{7} \] The cube root of 56 can be expressed as \( \sqrt[3]{8 \cdot 7} = \sqrt[3]{8} \cdot \sqrt[3]{7} = 2 \sqrt[3]{7} \), hence: \[ 2 \sqrt[3]{7} + 6 \sqrt[3]{7} = (2 + 6) \sqrt[3]{7} = 8 \sqrt[3]{7} \]
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256−−√3−47–√3: \[ \sqrt[3]{256} - 4 \sqrt[3]{7} \] Given that \( \sqrt[3]{256} = \sqrt[3]{4^4} = 4 \sqrt[3]{4} \), we would not be able to conclude directly, but it appears to not match \( 8 \cdot 3^{\sqrt{7}} \).
None of the simplified expressions matches \( 8 \cdot 3^{\sqrt{7}} \). Therefore, the correct answer is:
None of the given options simplifies to \( 8 \cdot 3^{\sqrt{7}} \).
1 answer