Certainly! Let's solve the expression [tex]\(\frac{1}{\sqrt[3]{16}}\)[/tex] step by step.
1. Determine the cube root of 16:
The cube root of a number [tex]\(a\)[/tex] is a number [tex]\(b\)[/tex] such that [tex]\(b^3 = a\)[/tex]. For this particular case, we need to find [tex]\(b\)[/tex] such that:
[tex]\[
b^3 = 16
\][/tex]
The cube root of 16 is approximately:
[tex]\[
\sqrt[3]{16} \approx 2.5198420997897464
\][/tex]
2. Calculate the reciprocal of the cube root:
Once we have the cube root of 16, we need to find its reciprocal. The reciprocal of a number [tex]\(x\)[/tex] is [tex]\( \frac{1}{x} \)[/tex].
So, we have:
[tex]\[
\frac{1}{\sqrt[3]{16}} = \frac{1}{2.5198420997897464}
\][/tex]
3. Compute the value:
Simplifying the reciprocal, we get:
[tex]\[
\frac{1}{2.5198420997897464} \approx 0.39685026299204984
\][/tex]
Thus, the value of [tex]\(\frac{1}{\sqrt[3]{16}}\)[/tex] is approximately:
[tex]\[
0.39685026299204984
\][/tex]
