$$ 3^{3/n}(\sqrt[n]{2}) $$

If \(n\) is a positive integer, which of the following is equivalent to the expression above?

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When the degree of the root is the same, we can combine the terms inside. For example, \( \sqrt{2}\cdot\sqrt{3}=\sqrt{6} \) . In our expression, the degree of the root is \(n\) for both bases.

We can confirm by rewriting as fractional exponents. The denominator of the exponent is equivalent to the degree of the root.

$$ 3^{3/n}(\sqrt[n]{2}) $$ $$ =3^{\frac{3}{n}}\cdot 2^{\frac{1}{n}} $$

This is the expression in radical form:

$$ \sqrt[n]{3^3} \cdot \sqrt[n]{2} $$ $$ = \sqrt[n]{3^3\cdot 2} $$ $$ =\boxed{\sqrt[n]{54}} $$