Answer
$\dfrac{1}{100}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\dfrac{2^{2/3}}{2000^{2/3}}
,$ use the laws of exponents.
$\bf{\text{Solution Details:}}$
Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^m}{z^p} \right)^q=\dfrac{x^{mq}}{z^{pq}},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\left(\dfrac{2}{2000}\right)^{2/3}
\\\\=
\left(\dfrac{1}{1000}\right)^{2/3}
.\end{array}
Using the definition of rational exponents which is given by $a^{\frac{m}{n}}=\sqrt[n]{a^m}=\left(\sqrt[n]{a}\right)^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\left(\sqrt[3]{\dfrac{1}{1000}}\right)^{2}
\\\\=
\left(\sqrt[3]{\left(\dfrac{1}{10}\right)^3}\right)^{2}
\\\\=
\left(\dfrac{1}{10}\right)^{2}
\\\\=
\dfrac{1}{100}
.\end{array}
