Please help with math questions

Hi, I can't figure out these two questions. ^ ^"

If (a + b) ^ (1/2) = (a - b) ^ (- 1/2), which of the following is true:

b = 0
a + b = 1
a - b = 1
a^2 + b^2 = 1
a^2 - b^2 = 1



If a and b are positive integers and ( a^(1/2)b^(1/3))^6 = 432, what is the value of ab?
6
12
18
24
36

1) try plugging things in

for b=0, it would end up a^(1/2)=a^(-1/2) which is not true

then for a+b=1 try substituting all b's for (1-a)

for a-b =1, substitute b for a +1

for a^2 + b^2 = 1, try raising each side to the fourth power, so 1 + 2ab = 1/(1+2ab) then
1 + 4ab + 4(a^2)(b^2) = 1, then 4ab = -4(a^2)(b^2), then ab = -1

for a^2-b^2 = 1, follow essentially the same process as the previous

2) the equation is just (a^3)(b^2) = 432
which is ((ab)^2) * a = 432
you can narrow down the choices by seeing which squares are less than 432 because if a square is bigger than 432 the value for ab is too big
then because they are pos. integers, you can narrow down the choices because some are too small
for the choices left, divide 432 by the square
remember, the quotient has to be a positive integer, a
if the previous quotient is a factor of the ab that was squared, that is the correct ab

(a + b) ^ (1/2) = (a - b) ^ (- 1/2),

b = 0

If a and b are positive integers and ( a^(1/2)b^(1/3))^6 = 432, what is the value of ab?
ab=3^(3/5)*2^(4/5)