Use Index Laws to simplify (a^-2)(b^(5/2) over square root of 36ab^3.

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We have to simplify
(a^-2)(b^5/2)/((36ab^3)^(1/2))

(a^-2)(b^5/2)/((36ab^3)^(1/2))

=>
(a^-2)(b^5/2)/[6a^(1/2)*b^(3/2)]

=> (a^(-2 -
1/2))(b^(5/2 - 3/2)/6

=>
a^(-5/2)*b/6

=>
b/(6*a^(5/2))

The simplified form of
(a^-2)(b^5/2)/[(36ab^3)^(1/2)) = b/(6*a^(5/2))