2 is the base and ([tex]\sqrt[4][a^5 b^3][/tex]) is the exponent.
the 4 is called an index and it means to fi d the fourth root of the expression under the ([tex]\sqrt[][text]) symbol.
a fourth root is a factor that was multiplied four times. ex: 2*2*2*2=16. the fourth root of 16 is two.
when you do square roots, you take the number representing the factor out of the radical. anything else that is not a square root stays under. ex:
([tex]\sqrt[9][text])
([tex]\sqrt[3*3*3][text]) there is one set of two 3's so
([tex]3\sqrt[3][text])
with a fourth root, you look for groups of four. the symbol of that group is placed outside the radical. anything else stays in.
([tex]\sqrt[4][a^5 b^3][/tex])
([tex]\sqrt[4][a*a*a*a*a*b*b*b][/tex]) there is one group of 4 a's so
([tex]a\sqrt[4][a* b^3][/tex])
there really isn't anything else to do to simplify the expression
