College

What is the cube root of [tex]$8x^{27}$[/tex]?

A. [tex]$2x^3$[/tex]
B. [tex]$2x^9$[/tex]
C. [tex]$4x^3$[/tex]
D. [tex]$4x^9$[/tex]

Answer :

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

1. Cube Root of 8:
- The cube root of 8 is 2 because [tex]\(2^3 = 8\)[/tex].

2. Cube Root of [tex]\(x^{27}\)[/tex]:
- To find the cube root of [tex]\(x^{27}\)[/tex], you take the exponent 27 and divide it by 3.
- So, [tex]\((x^{27})^{1/3} = x^{27/3} = x^9\)[/tex].

Now, combine both parts:

- The cube root of [tex]\(8x^{27}\)[/tex] is [tex]\(2 \times x^9\)[/tex], which simplifies to [tex]\(2x^9\)[/tex].

Thus, the correct answer is [tex]\(2x^9\)[/tex].