Answer :

To find the cube root of the expression [tex]\( 8x^{27} \)[/tex], we will break it down into manageable parts: the coefficient and the variable.

1. Cube Root of the Coefficient:

The coefficient is 8. The cube root of 8 is calculated as:

[tex]\[
\sqrt[3]{8} = 2
\][/tex]

So, the cube root of the coefficient 8 is 2.

2. Cube Root of the Variable Part:

The variable part is [tex]\( x^{27} \)[/tex]. To find the cube root, we divide the exponent by 3:

[tex]\[
\sqrt[3]{x^{27}} = x^{27/3} = x^9
\][/tex]

3. Combining the Results:

The cube root of the entire expression [tex]\( 8x^{27} \)[/tex] is the product of the cube roots we found:

[tex]\[
\sqrt[3]{8x^{27}} = 2 \cdot x^9 = 2x^9
\][/tex]

Therefore, the correct answer is [tex]\( 2x^9 \)[/tex]. This matches option 2 from the provided choices.

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