Question

Which expression simplifies to 8 3^√7?

negative 6 cube root of 7 minus 2 cube root of 7

3 cube root of 6 plus 5 cube root of 1

cube root of 56 plus 6 cube root of 7

256−−√3−47–√3

Answer 1

To determine which expression simplifies to \( 8 \cdot 3^{\sqrt{7}} \), let's simplify each of the given options step by step:

1. **Negative 6 cube root of 7 minus 2 cube root of 7:**
\[
-6 \sqrt[3]{7} - 2 \sqrt[3]{7} = (-6 - 2) \sqrt[3]{7} = -8 \sqrt[3]{7}
\]

2. **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 \( 8 \cdot 3^{\sqrt{7}} \).

3. **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:
\[
2 \sqrt[3]{7} + 6 \sqrt[3]{7} = (2 + 6) \sqrt[3]{7} = 8 \sqrt[3]{7}
\]

4. **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 \( 8 \cdot 3^{\sqrt{7}} \).