Which of the following expressions is equivalent to (\root(3)(216))/(27^((1)/(3))) when applying the exponent properties?

1/2
18
2
8

1 answer

To simplify the expression \(\frac{\sqrt[3]{216}}{27^{\frac{1}{3}}}\), we can start by rewriting each part using exponent properties.

First, we can rewrite \( \sqrt[3]{216} \) and \( 27^{\frac{1}{3}} \):

  1. Calculating \(\sqrt[3]{216}\): \[ 216 = 6^3 \] Therefore, \[ \sqrt[3]{216} = \sqrt[3]{6^3} = 6. \]

  2. Calculating \(27^{\frac{1}{3}}\): \[ 27 = 3^3 \] Thus, \[ 27^{\frac{1}{3}} = \sqrt[3]{27} = \sqrt[3]{3^3} = 3. \]

Putting it all together: \[ \frac{\sqrt[3]{216}}{27^{\frac{1}{3}}} = \frac{6}{3} = 2. \]

Thus, the expression \(\frac{\sqrt[3]{216}}{27^{\frac{1}{3}}}\) simplifies to \(2\).

The equivalent answer is: \[ \boxed{2}. \]