Answer
$\color{blue}{\dfrac{\sqrt[4]{7}+\sqrt[4]{9}t^2}{t^3}}$
Work Step by Step
Simplify each radical term to obtain:
$=\sqrt[4]{\dfrac{7}{(t^3)^4}}+\sqrt[4]{\dfrac{9}{t^4}}
\\=\dfrac{\sqrt[4]{7}}{t^3}+\dfrac{\sqrt[4]{9}}{t}$
Make the terms similar using their LCD of $t^3$ to obtain:
$=\dfrac{\sqrt[4]{7}}{t^3}+\dfrac{\sqrt[4]{9}(t^2)}{t(t^2)}
\\=\dfrac{\sqrt[4]{7}}{t^3}+ \dfrac{\sqrt[4]{9}t^2}{t^3}$
Add the numerators and retain the denominator to obtain:
$=\color{blue}{\dfrac{\sqrt[4]{7}+\sqrt[4]{9}t^2}{t^3}}$
