Question

1. choose the correct expression.

$14^{\frac{1}{4}}$
$\sqrt14{\frac{1}{4}}$
$\sqrt4{14}$
$\sqrt{14^4}$

1. simplify.

$5^0$
$\frac{1}{5}$
$5$
$1$
$0$

Explanation:

Step1: Recall exponent - root relation

The formula for converting a rational exponent to a radical is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (when \(n\gt0\)). For the expression \(14^{\frac{1}{4}}\), here \(a = 14\), \(m = 1\) and \(n=4\).

Step2: Apply the formula

Using the formula \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\), substituting \(a = 14\), \(m = 1\) and \(n = 4\), we get \(\sqrt[4]{14^{1}}=\sqrt[4]{14}\).

Answer:

\(\boldsymbol{\sqrt[4]{14}}\) (the option with \(\sqrt[4]{14}\))