Answer
$y$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
y^{7/3}\cdot y^{-4/3}
.$
$\bf{\text{Solution Details:}}$
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
y^{\frac{7}{3}+\left(-\frac{4}{3} \right)}
\\\\=
y^{\frac{7}{3}-\frac{4}{3}}
\\\\=
y^{\frac{3}{3}}
\\\\=
y^{1}
\\\\=
y
.\end{array}
