Explain why 36^-1/2 is equal to 1/6...?

First, applying the power of 1/2 is a square root.
So 36^1/2 = 6.

Next, the power of -1 is to invert the numerator and denominator.
So 36^-1/2 = 1/6

36^(-1/2) = 1 / 36^(1/2) = 1 / 6----------agreed !

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36^(-1/2)
= √[36^(-1)]
= √[1/(36^1)]
= √[1/(6^2)]
= 1/6

If you multiply it by 36^(1/2), the rule for multiplying powers of the same base (add the exponents) gives
36^0
which is 1.
Since 36^(1/2) = 6, we have
[36^(-1/2)] * 6 = 1
therefore
36^(-1/2) = 1/6

Do you need to explain why 36^(1/2) = 6?
It's because [36^(1/2)]^2 = 36^((1/2)*2) = 36^1 = 36

And why does 36^0 = 1?
Because 36^0 * 36^1 = 36^(0+1) = 36^1
divide both sides by 36^1:
36^0 = 1.

6^(-2/2)=6^(-1)=1/6