if a and b are positive integers and (a^(1/2)b^(1/3))^6 = 432, what is the value of ab?
If someone could show me step by step how to solve this I'd appreciate it soo much
2007-11-30 15:41:43 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
thanks guys!
2007-11-30 15:55:44 · update #1
are you cheating?
2007-11-30 15:45:18 · answer #1 · answered by Anonymous · 0⤊ 2⤋
(a^(1/2)b^(1/3))^6 = a^3*b^2 = 432 = 9*48 = 3^3 * 4^2
a = 3, b = 4
ab = 3*4 = 12
2007-11-30 15:50:34 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋
432= 4 x 4 x 3 x 3 x 3
(a^(1/2)b^(1/3))^6
= (a^(6/2))(b^(6/3))
= (a^3)(b^2)
Therefore a=3, b=4
ab=12
2007-11-30 15:49:34 · answer #3 · answered by vcs7578 5 · 0⤊ 0⤋
(a^(1/2)b^(1/3))^6 = a^3 * b^2 = 432.
432 = 2^4 * 3^3 = 3^3 * 4^2.
So a = 3, b = 4, ab=12.
2007-11-30 15:53:12 · answer #4 · answered by xiaodao 4 · 0⤊ 0⤋
[a^(1/2)*b^(1/3)]^6 = a^(6/2)*b^(6/3) = a³b² = 432
Therefore:
a³b² = 432
432 = 27*16 = (3³)(4²) = a³b²
a = 3
b = 4
ab = 3*4 = 12
2007-11-30 15:51:51 · answer #5 · answered by Northstar 7 · 0⤊ 0⤋
aww man is this really gonna be on there?? =[ im taking mine tomorrow
2007-11-30 15:45:11 · answer #6 · answered by joanna 3 · 0⤊ 2⤋