Question

question

simplify: \\(\sqrt7{128a^{14}}\\).

provide your answer below:

Explanation:

Factor the radicand into perfect seventh powers

$$
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$$

Apply the product rule for radicals

$$ \sqrt[7]{128a^{14}} = \sqrt[7]{2^7 \cdot (a^2)^7} $$

Simplify the radical expression

$$ \sqrt[7]{2^7} \cdot \sqrt[7]{(a^2)^7} = 2a^2 $$

Answer:

\(2a^2\)