" (iv) "m^(3)root(6)(n^(3))

Simplify : [root(3)root(6)(5^(9))]^(4)[root(3)root(6)(5^(9)]]^(4)

Evaluate: (6^(2/3) xx root(3)((6)^(7)))/(root(3)(6^(6)))

Simplify [root(3)(root(6)(2^(9)))]^(4)xx[root(6)(root(3)(2^(9)))]^(4) .

Simplify: [root(3)(root(6)(5^(9)))]^(8)[root(6)(root(3)(5^(9)))]^(8)

The following are the steps involved in finding the greatest among root(3)(2),root(6)(3) and sqrt(6) . Arrange them in sequential order. (A) The LCM of the denominators of the exponents is 6. (B) therefore root(6)(216) i.e., sqrt(6) is greatest. (C) root(3)(2)=2^(1//3), root(6)(3)=3^(1//6), sqrt(6)=6^(1//2) (D) 2^(1//3)=2^(2//6), 3^(1//6), 6^(1//2)=6^(3//6) (E) root(3)(2)=root(6)(4)root(6)(3)-root(6)(3),sqrt(6)=root(6)(216)

sqrt(m^(2)n^(2))times root(6)(m^(2)n^(2))times root(3)(m^(2)n^(2))

If 'm' and 'n' are the roots of the equation x^(2) - 6x +2=0 , find the value of m^(3)n^(2)+n^(3)m^(2) :