Following the rules for exponents this problem can be rewritten as:
First color(red)(X^n*Y^n = XY^n)Xn⋅Yn=XYn; we can apply this to the terms within parenthesis:
(10^(3/4)*4^(3/4))^-4 -> ((4*10)^(3/4))^-4 -> (40^(3/4))^-4(1034⋅434)−4→((4⋅10)34)−4→(4034)−4
Next color(red)((X^n)^m = X^(n*m))(Xn)m=Xn⋅m can be apply to our simplification:
(40^(3/4))^-4 -> 40^((3/4)*-4) -> 40^-3(4034)−4→40(34)⋅−4→40−3
Finally, color(red)(X^-n = 1/X^n)X−n=1Xn can applied to give:
40^-3 -> 1/40^3 -> 1/(40*40*40) -> 1/6400040−3→1403→140⋅40⋅40→164000
