^{5}√(5)^{3}√(x)
To write this expression as a single radical, we must find a way to express the terms with the same type of root so that we may multiply them together. First, we rewrite the terms with fractional exponents.
5^{1/5}x^{1/3}
Given that the denominator represents the type of root, we can multiply the terms by finding the lowest common denominator of their exponents. For 3 and 5 this is 15, so we rewrite both of our terms with exponents that have a denominator of 15.
5^{3/15}x^{5/15}
Now we can switch back to radical notation
^{15}√(5^{3})^{15}√(x^{5})
With the same type of root we can multiply these
^{15 }√(5^{3}x^{5})
And further simplifying the term 5^{3 }gives the answer
^{15}√(125x^{5})
10/4/2013

William R.