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Answer :
To find the cube root of the expression [tex]\(8x^{27}\)[/tex], let's break it down step by step:
1. Understand the expression: The expression given is [tex]\(8x^{27}\)[/tex]. We are tasked with finding the cube root of this expression.
2. Cube root of constants: First, let's take the cube root of the constant part, which is 8. The cube root of 8 is 2, because [tex]\(2^3 = 8\)[/tex].
3. Cube root of the variable term: Now, let's find the cube root of [tex]\(x^{27}\)[/tex]. To do this, remember that [tex]\(\sqrt[3]{x^n} = x^{n/3}\)[/tex]. So, the cube root of [tex]\(x^{27}\)[/tex] is [tex]\(x^{27/3} = x^9\)[/tex].
4. Combine the results: Combining both parts together, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Therefore, the correct answer is [tex]\(2x^9\)[/tex].
1. Understand the expression: The expression given is [tex]\(8x^{27}\)[/tex]. We are tasked with finding the cube root of this expression.
2. Cube root of constants: First, let's take the cube root of the constant part, which is 8. The cube root of 8 is 2, because [tex]\(2^3 = 8\)[/tex].
3. Cube root of the variable term: Now, let's find the cube root of [tex]\(x^{27}\)[/tex]. To do this, remember that [tex]\(\sqrt[3]{x^n} = x^{n/3}\)[/tex]. So, the cube root of [tex]\(x^{27}\)[/tex] is [tex]\(x^{27/3} = x^9\)[/tex].
4. Combine the results: Combining both parts together, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Therefore, the correct answer is [tex]\(2x^9\)[/tex].
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