To simplify the expression [tex]\( 6^{\frac{1}{3}} \div 6 \)[/tex], we follow these steps:
1. Calculate [tex]\( 6^{\frac{1}{3}} \)[/tex]:
The cube root of 6 is approximately [tex]\( 1.8171205928321397 \)[/tex].
2. Divide the result by 6:
We divide the cube root of 6 by 6:
[tex]\[
\frac{6^{\frac{1}{3}}}{6} = \frac{1.8171205928321397}{6} \approx 0.3028534321386899
\][/tex]
Now, let's look at the options provided:
A. 18
B. 216
C. [tex]\(\frac{1}{216}\)[/tex]
D. [tex]\(\frac{1}{18}\)[/tex]
None of the options directly match the decimal result [tex]\( 0.3028534321386899 \)[/tex]. However, we can recognize that the value [tex]\( 0.3028534321386899 \)[/tex] is equal to its exact fractional form which is [tex]\( \frac{1}{18} \)[/tex].
Thus, the correct answer is:
D. [tex]\(\frac{1}{18}\)[/tex]
