Question

$\sqrt4{16x^3}$

Explanation:

Step1: Simplify the radical

First, we can rewrite \( 16 \) as \( 2^4 \). So the expression becomes \( \sqrt[4]{2^4 x^3} \).

Step2: Apply the fourth - root property

Using the property \( \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b} \) (where \( a = 2^4 \) and \( b=x^3 \)) and \( \sqrt[n]{a^n}=a \) (for \( n = 4 \) and \( a = 2 \)), we get \( \sqrt[4]{2^4}\cdot\sqrt[4]{x^3}=2\sqrt[4]{x^3} \).

Answer:

\( 2\sqrt[4]{x^{3}} \)