Question

use the product rule to multiply. assume that all vari
\sqrt4{2x^{3}}\cdot\sqrt4{9}
\sqrt4{2x^{3}}\cdot\sqrt4{9}=\square
(type an exact answer, using radicals as needed. sim

Explanation:

Step1: Recall the product rule for radicals

The product rule for radicals states that \(\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{ab}\) when \(n\) is a positive integer and \(a,b\) are non - negative real numbers (in the context of real - valued radicals). Here, \(n = 4\), \(a=2x^{3}\) and \(b = 9\).
So, \(\sqrt[4]{2x^{3}}\cdot\sqrt[4]{9}=\sqrt[4]{(2x^{3})\times9}\)

Step2: Simplify the expression inside the radical

Multiply the terms inside the fourth - root: \((2x^{3})\times9 = 18x^{3}\)
So, \(\sqrt[4]{(2x^{3})\times9}=\sqrt[4]{18x^{3}}\)

Answer:

\(\sqrt[4]{18x^{3}}\)