Answer:
Step-by-step explanation:
To evaluate (4/9) raised to the power of -1/2, we need to apply the rules of exponents.
First, let's understand the meaning of a negative exponent. When we have a negative exponent, it indicates that we need to take the reciprocal (or inverse) of the base raised to the positive exponent.
In this case, we have (4/9) raised to the power of -1/2. To evaluate it, we need to find the reciprocal of (4/9) raised to the power of 1/2.
To find the reciprocal, we can simply swap the numerator and denominator of (4/9).
So, the reciprocal of (4/9) is (9/4).
Next, we need to find the square root of (9/4), which is the same as raising (9/4) to the power of 1/2.
To raise (9/4) to the power of 1/2, we take the square root of both the numerator and the denominator:
√(9/4) = √9 / √4 = 3/2.
Therefore, (4/9) raised to the power of -1/2 is equal to the reciprocal of 3/2, which is 2/3.
So, (4/9)^(-1/2) = 2/3.
