Answer :
To find the cube root of [tex]\(8x^{27}\)[/tex], let's break it down step by step:
1. Identify the cube root components:
- We have the expression [tex]\(8x^{27}\)[/tex].
- The number 8 can be written as [tex]\(2^3\)[/tex].
2. Apply cube root to each part:
- The cube root of [tex]\(8\)[/tex] (which is [tex]\(2^3\)[/tex]) is [tex]\(2\)[/tex].
- The expression [tex]\(x^{27}\)[/tex] can be rewritten as [tex]\((x^9)^3\)[/tex].
- The cube root of [tex]\((x^9)^3\)[/tex] is [tex]\(x^9\)[/tex].
3. Combine the results:
- Combining the results from the cube roots of [tex]\(8\)[/tex] and [tex]\(x^{27}\)[/tex], we get [tex]\(2x^9\)[/tex].
Therefore, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
1. Identify the cube root components:
- We have the expression [tex]\(8x^{27}\)[/tex].
- The number 8 can be written as [tex]\(2^3\)[/tex].
2. Apply cube root to each part:
- The cube root of [tex]\(8\)[/tex] (which is [tex]\(2^3\)[/tex]) is [tex]\(2\)[/tex].
- The expression [tex]\(x^{27}\)[/tex] can be rewritten as [tex]\((x^9)^3\)[/tex].
- The cube root of [tex]\((x^9)^3\)[/tex] is [tex]\(x^9\)[/tex].
3. Combine the results:
- Combining the results from the cube roots of [tex]\(8\)[/tex] and [tex]\(x^{27}\)[/tex], we get [tex]\(2x^9\)[/tex].
Therefore, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
