Final answer:
The expression ((4/9)⁻¹⁄²) is evaluated by first finding the reciprocal (9/4) and then taking the square root, which results in the answer 3/2. Thus, the evaluation gives us the answer (a) 3/2.
Step-by-step explanation:
To evaluate the expression (4/9)⁻¹⁄², we need to interpret the negative and the fractional exponents. The negative exponent tells us to take the reciprocal of the base, which in this case is 4/9. Next, the exponent of 1/2, which is equivalent to a square root, is applied to that reciprocal.
Firstly, we find the reciprocal of 4/9, which is 9/4. Then, taking the square root of 9/4 gives us 3/2 because the square root of 9 is 3 and the square root of 4 is 2.
To evaluate (4/9)⁻¹/², we can simplify the expression step-by-step. First, let's calculate the reciprocal of 4/9, which is 9/4. Next, let's simplify 9/4 raised to the power of 1/2. Taking the square root of 9 gives us 3, and the square root of 4 gives us 2. Therefore, (4/9)⁻¹/² is equal to 3/2.
Thus, the evaluation gives us the answer (a) 3/2.