Question

Please explain how to solve this (tle=" \sqrt[4]{a^5 b^3} " alt=" \sqrt[4]{a^5 b^3} " align="absmiddle" class="latex-formula">)²

Answer 1

2 is the base and ($\sqrt[4][a^5 b^3]$) is the exponent.

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

($\sqrt[4][a*a*a*a*a*b*b*b]$) there is one group of 4 a's so

($a\sqrt[4][a* b^3]$)

there really isn't anything else to do to simplify the expression