1. [3x^(5/2)]-9=0
2. [(x^2+9x+22)]^(3/2)=8
3. [(2x+3)]^(1/2)=4
4. [(5x-5)]^(2/3)=16
I'll do one of them. They are all quite similar. Then come back and let us know where you get stuck, if you do.
#2: (x^2+9x+22)^(3/2) = 8
Take both sides to the 2/3 power, since 3/2 * 2/3 = 1:
[(x^2+9x+22)^(3/2)]^(2/3) = 8^(2/3)
since 8= 2^3, 8^2/3 = 4 and we have
x^2+9x+22 = 4
x^2+9x+18 = 0
(x+3)(x+6) = 0
x = -3 or -6
check:
-3: 9-27+22 = 4; 4^3/2 = 8: ok
-6: 36-54+22= 4: ok