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Answer :
To find the cube root of the expression [tex]\(8x^{27}\)[/tex], let's break down the problem step by step:
1. Understanding Cube Roots:
The cube root of a number or expression is another number or expression that, when multiplied by itself three times, gives the original number or expression. In mathematical terms, if [tex]\(a^3 = b\)[/tex], then [tex]\(a\)[/tex] is the cube root of [tex]\(b\)[/tex].
2. Cube Root of 8:
- The cube root of [tex]\(8\)[/tex] is [tex]\(2\)[/tex] because [tex]\(2^3 = 8\)[/tex].
3. Cube Root of [tex]\(x^{27}\)[/tex]:
- When you're taking the cube root of an exponent, you divide the exponent by 3.
- Therefore, the cube root of [tex]\(x^{27}\)[/tex] is [tex]\(x^{27/3} = x^9\)[/tex].
4. Combine the Results:
- So, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Thus, the answer to the given question is [tex]\(2x^9\)[/tex].
1. Understanding Cube Roots:
The cube root of a number or expression is another number or expression that, when multiplied by itself three times, gives the original number or expression. In mathematical terms, if [tex]\(a^3 = b\)[/tex], then [tex]\(a\)[/tex] is the cube root of [tex]\(b\)[/tex].
2. Cube Root of 8:
- The cube root of [tex]\(8\)[/tex] is [tex]\(2\)[/tex] because [tex]\(2^3 = 8\)[/tex].
3. Cube Root of [tex]\(x^{27}\)[/tex]:
- When you're taking the cube root of an exponent, you divide the exponent by 3.
- Therefore, the cube root of [tex]\(x^{27}\)[/tex] is [tex]\(x^{27/3} = x^9\)[/tex].
4. Combine the Results:
- So, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Thus, the answer to the given question is [tex]\(2x^9\)[/tex].
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