I think I understand what you're wanting. You want to turn that square root problem into one with a fraction as an exponent. If that's the case, the steps to do that are this:
[tex](5 \sqrt{ x^{7} } ) ^{3} [/tex]
First start out by simplfiying the square root of [tex] x^{7} [/tex]
[tex] \sqrt[2]{ x^{7} } [/tex] in fraction form pulls the 2, which is called the index over as the denominator in the exponent, with the 7 being the numerator. So that expression as a square root looks like this as an rational exponent:
[tex] x^{ \frac{7}{2} } [/tex]
But we still have the 5 to content with, so let's add that in there:
[tex][5( x^{ \frac{7}{2} } )] ^{3} [/tex]
not only is the exponent cubed now by multiplication, so is the 5:
[tex]125 x^{ \frac{21}{2} } [/tex]
