To determine which expression is equivalent to the given expression, we need to compare it against each of the provided options:
The expression to simplify is: [tex]\( x^{\frac{1}{6}} \)[/tex].
Option A: [tex]\( \frac{x^6}{6} \)[/tex]
- This does not match [tex]\( x^{\frac{1}{6}} \)[/tex] because [tex]\( \frac{x^6}{6} \)[/tex] represents dividing [tex]\( x \)[/tex] raised to the sixth power by 6, which is a completely different operation than raising [tex]\( x \)[/tex] to the one-sixth power.
Option B: [tex]\( x^{\frac{1}{6}} \)[/tex]
- This matches exactly. It's the same expression as the one we started with.
Option C: [tex]\( \frac{6}{x^5} \)[/tex]
- This represents a fraction where the numerator is 6 and the denominator is [tex]\( x \)[/tex] raised to the fifth power. This expression is not equivalent to [tex]\( x^{\frac{1}{6}} \)[/tex].
Option D: [tex]\( x \)[/tex]
- This represents [tex]\( x \)[/tex] raised to the first power. This is not equivalent to [tex]\( x^{\frac{1}{6}} \)[/tex].
Given these comparisons, the correct choice that matches the expression [tex]\( x^{\frac{1}{6}} \)[/tex] is:
B. [tex]\( x^{\frac{1}{6}} \)[/tex]
