Posted by Sam' on .
Rational Exponet Equations:
Help?
1.(x^2+9x+22)^3/2 = 8
2.(5x5)^2/3 = 16

Algebra2 
Reiny,
1.
raise both sides to the 2/3 , notice that 2/3 is the reciprocal of 3/2
[ (x^2 + 9x + 22)^(3/2) ] ^(2/3) = 8^(2/3)
(x^2 + 9x + 22)^1 = 8^(2/3)
x^2+9x+22 = 4
x^2 + 9x + 18 = 0
(x+6)(x+3) = 0
x = 6 or x = 3
Since we effectively squared both sides, ( ^(2/3) is the same as taking the cube root, then squaring), all answers must be verified.
if x = 6
LS = (36  54 + 22)^(3/2
= 4^(3/2) = 8
= RS
if x=3
LS = (927+22)^(3/2)
= 4^(3/2) = 8
= RS
so x=6 or x=3
You try the second one in the same way.