Homework Help

simplify ∛108a^16b^9

user profile pic

connorcolin3 | Valedictorian

Posted December 23, 2012 at 11:49 PM via web

dislike 0 like

simplify ∛108a^16b^9

Tagged with algebra/trig, math

1 Answer | Add Yours

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted December 24, 2012 at 12:20 AM (Answer #1)

dislike 1 like

cubic root can be given as a power of (1/3).

`root(3)(108a^16b^9)`

`= root(3)(108)*root(3)(a^16)*root(3)(b^9)`

`= (108)^(1/3)*(a^16)^(1/3)*b^9(1/3)`

`= (27*4)^(1/3)*(a^9*a^7)^(1/3)*b^9(1/3)`

`= (3^3*4)^(1/3)*(a^15*a^2)^(1/3)*b^9(1/3)`

`= 3*4^(1/3)*a^5*a^(2/3)*b^3`

`= 3a^5b^3*a^(2/3)*4^(1/3)`

`= 3a^5b^3root(3)(a^2*4)`

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes