Answer :

The first step for solving this expression is to know that the root of a product is equal to the product of the roots of each factor. Knowing this,, the expression becomes the following:
[tex] \sqrt[3]{27} \sqrt[3]{ x^{9} } [/tex]
Write the number in the first square root in exponential form with a base of 3.
[tex] \sqrt[3]{ 3^{3} } \sqrt[3]{ x^{9} } [/tex]
Now reduce the index of the radical and exponent in the second square root with 3.
[tex] \sqrt[3]{ 3^{3} } [/tex] x³
Lastly,, reduce the index of the radical and exponent with 3 to get your final answer.
3x³
This means that the correct answer to your question will be option B.
Let me know if you have any further questions.
:)

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Rewritten by : Barada

The value of the expression ∛27x⁹ is 9x³.

The given expression is ∛27x⁹.

Cube root of twenty seven times of x power nine.

We can split the terms inside the cube root.

27=3×3×3

∛x⁹ = x³

Now let us plug in the above expression.

= 3√3³ × x⁹

= 3√3³ × √ x⁹

= 3 × 3 × x³

= 9x³.

Hence, the value of the expression ∛27x⁹ is 9x³.

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