Question

current objective
use the quotient property to simplify expressions

question

simplify: \\(\sqrt4{\frac{324w^9}{w^2}}\\).

provide your answer below:

Explanation:

Simplify the fraction inside the radical

$$ \frac{324w^9}{w^2} = 324w^{9-2} = 324w^7 $$

Factor the expression into perfect fourth powers

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Apply the product property of radicals to simplify

$$ \sqrt[4]{324w^7} = \sqrt[4]{3^4 \cdot 4 \cdot w^4 \cdot w^3} = 3w\sqrt[4]{4w^3} $$

Answer:

\(3w\sqrt[4]{4w^3}\)