QT - exponents or indices

1. b

2.20/3

3.a = 1

therefore,a^3+3a+-2

= 1+3-2

= 2

4. is a cyclical simplification so it reduces 1.

3. a + (2^0.5 -1 )^(1/3 ) = (2^0.5 +1)^(1/3) if we cube on both sides we get a^3 + 2^0.5 -1 +3*a*(2^0.5 -1 )^(1/3 )*(a + (2^0.5 -1 )^(1/3 )) = 2^0.5 + 1 implies a^3 + 2^0.5 -1 +3*a*(2^0.5 -1 )^(1/3 )*((2^0.5 +1)^(1/3)) = 2^0.5 + 1 implies a^3 +3a -2 = 0;

4. numerator:x^(a/(a-b) - a/(a+b)) = x^(2ab/(a^2-b^2))

similarly denominator is x^(2ab/(b^2 - a^2)) so total fraction is x^(4ab/(a^2-b^2)) so fraction power a+b is x^(4ab/(a-b))

2. a^2  = 3^0.5 +3^-0.5 +2 b^2 = 3^0.5 + 3^-0.5 -2 a^2 + b^2 = 2(3^0.5 + 3^-0.5) (a^2 + b^2)^2 = 4(3 + 1/3 + 2) = 64/3