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: