# 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))**

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

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

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

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

= b/(6a^5/2)