Question

use the product rule to multiply. assume that
\\(\sqrt4{6x^3} \cdot \sqrt4{7}\\)
\\(\sqrt4{6x^3} \cdot \sqrt4{7} = \square\\)
(type an exact answer, using radicals as need

Explanation:

Step1: Apply radical product rule

The product rule for radicals states $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}$. Apply this to the given expression:
$$\sqrt[4]{6x^3} \cdot \sqrt[4]{7} = \sqrt[4]{6x^3 \cdot 7}$$

Step2: Multiply the constant terms

Calculate the product of 6 and 7 inside the radical:
$$\sqrt[4]{6 \cdot 7 \cdot x^3} = \sqrt[4]{42x^3}$$

Answer:

$\sqrt[4]{42x^3}$