What is the value of [ 1 2 ⁻¹ ( 2 3 ) ] ?

Step-by-step solution

Let = ⁻¹ ( 2 3 ) = 2 3 = 6 The given expression becomes ( 1 2 ) = ( 12 ) ( 12 ) = (15^ ) = (45^ - 30^ ) Using the formula (A - B) = A - B 1 + A B (15^ ) = 45^ - 30^ 1 + 45^ 30^ (15^ ) = 1 - 1 3 1 + 1 3 = 3 - 1 3 + 1 Rationalizing the denominator: (15^ ) = ( 3 - 1)^2 ( 3 + 1)( 3 - 1) = 3 + 1 - 2 3 3 - 1 (15^ ) = 4 - 2 3 2 = 2 - 3 Answer: 2 - 3