Answer :
To find the cube root of [tex]\(8x^{27}\)[/tex], we'll break the expression into two parts: the numerical part and the variable part.
1. Numerical Part:
- The cube root of 8.
- Since [tex]\(2^3 = 8\)[/tex], the cube root of 8 is 2.
2. Variable Part:
- Look at [tex]\(x^{27}\)[/tex].
- When you're taking the cube root of an expression with exponents, you divide the exponent by 3.
[tex]\[
\text{Cube root of } x^{27} = x^{27/3} = x^9
\][/tex]
Now, combine the results from both parts:
- The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Thus, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(\boxed{2x^9}\)[/tex].
1. Numerical Part:
- The cube root of 8.
- Since [tex]\(2^3 = 8\)[/tex], the cube root of 8 is 2.
2. Variable Part:
- Look at [tex]\(x^{27}\)[/tex].
- When you're taking the cube root of an expression with exponents, you divide the exponent by 3.
[tex]\[
\text{Cube root of } x^{27} = x^{27/3} = x^9
\][/tex]
Now, combine the results from both parts:
- The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2x^9\)[/tex].
Thus, the cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(\boxed{2x^9}\)[/tex].
