High School

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

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

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].