Questions: Use the quotient rule to divide. Then simplify if possible. (3 √[4]162) / (√[4]2)

Solution Steps

We start with the expression: \[ \frac{3 \sqrt[4]{162}}{\sqrt[4]{2}} \]

Using the quotient rule for roots, we can rewrite the expression as: \[ \sqrt[4]{\frac{162^3}{2}} \]

Calculating the radicands, we have: \[ \frac{162^3}{2} = 9 \cdot 2^{1/4} \] Thus, the expression simplifies to: \[ \sqrt[4]{9 \cdot 2^{1/4}} = 9 \]

Final Answer