Hello, ^_^Engineer_Adam^_^
You have too many braces . . .
You typed:
[math ] \sqrt[n]{\frac{a}{b}}\:\:=\:\:\frac{ {\sqrt[n]{a}} {\sqrt[n]{b}} }\;\;\mbox{such that a and b}>\:0\:[/tex]
and produced this:
Eliminate the red braces above:
[math ] \sqrt[n]{\frac{a}{b}}\:\:=\:\:\frac {\sqrt[n]{a}} {\sqrt[n]{b}}\;\;\mbox{such that a and b}>\:0\:[/tex]
which produces: