This says to simplify (4^1/3 x 4^2/6)^3/11 over (4^5/6)^3/11

Question

I already know the answer but I have no idea how they got it. The answer was (1/4)^3/66 but I have no idea how they got it. Could someone explain?

Answer 1

First adds the exponents: 1/3 + 2/6 = 2/6+2/6 = 4/6 = 2/3

Multiplies that by 3/11, to get 2/3*3/11 = 2/11 numerator done

denominator multiplies 5/6 * 3/11 = 15/66

so subtracting these two resulsts: 2/11 - 15/66 = 12/66 - 15/66 = -3/66

So the answer is 4 ^ (-3/66) = (1/4) ^(3/66) = (1/4)^(1/22)