Question

which expression is equivalent to \\(\sqrt4{3}\\)? \\(4^{\frac{1}{3}}\\) \\(3^{\frac{1}{4}}\\) \\(4^{3}\\) \\(3^{4}\\)

Explanation:

Step1: Recall the radical to exponent rule

The rule for converting a radical to a rational exponent is $\sqrt[n]{a}=a^{\frac{1}{n}}$.

Step2: Apply the rule to the given radical

For the expression $\sqrt[4]{3}$, here $n = 4$ and $a = 3$. Using the rule $\sqrt[n]{a}=a^{\frac{1}{n}}$, we substitute the values: $\sqrt[4]{3}=3^{\frac{1}{4}}$.

Answer:

$3^{\frac{1}{4}}$ (corresponding to the option $3^{\frac{1}{4}}$)