Thenumber 27 is a perfect cube. 3 is the cuberootof 27 and can be written with exponent as 27 = 3^{3}.
Powerrule can be used to simplify both the numerator and the denominator.In this case can be expressed as which is equal to .In the denominator, the new exponent would be 3 * (1/3) = 1.
Quotientrulecan be used to simplify the terms into one or eliminating thefraction form since the base is the same. Using the Quotient rule,the exponent can be simplified to 2 – (1) = 1.
Thereciprocalof the base number and the exponent eliminates the negative sign.
Thefinal answer is 1/3 which is the PrincipalRootof

^{1/2 }(ab^{1/2})
^{1/2}(ab^{1/2})Power rule is used to distribute the exponent to the inner exponents.The exponent of the expression can be written as (1/2) * (1/2) = ¼.
)^{}(ab^{1/2})Productrulecan be used to multiply components with the same base. Using theproduct rule, the exponent of a will be (1/4) + (1) = 5/4 and theexponent of b will be (1/2) + (1/2) = 1
Thefinal answer is which is the PrincipalRootof^{1/2}(ab^{1/2}).