Answer
$4$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents and the definition of rational exponents to simplify the given expression, $
\dfrac{64^{5/3}}{64^{4/3}}
.$
$\bf{\text{Solution Details:}}$
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
64^{\frac{5}{3}-\frac{4}{3}}
\\\\=
64^{\frac{1}{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}
\sqrt[3]{64^1}
\\\\=
\sqrt[3]{64}
\\\\=
\sqrt[3]{4^3}
\\\\=
4
.\end{array}
