simplify 9^-1/2/27^2/3 a). 1 b). 1/2 c). 1/9 d). 1/27?
To simplify the expression 9^(-1/2) / 27^(2/3), we need to use the properties of exponents to simplify the bases separately and divide the results.
First, let's simplify the base 9^(-1/2):
To do this, we can rewrite 9^(-1/2) as the reciprocal of the square root of 9, which is 1/√9. The square root of 9 is 3 since √9 = 3.
Therefore, 9^(-1/2) = 1/√9 = 1/3.
Next, let's simplify the base 27^(2/3):
To do this, we can rewrite 27^(2/3) as the cube root of 27 squared.
The cube root of 27 is 3 since ∛27 = 3.
Therefore, 27^(2/3) = (∛27)^2 = 3^2 = 9.
Now that we have simplified the bases, we can divide the results:
(9^(-1/2)) / (27^(2/3)) = (1/3) / 9 = 1/3 * 1/9 = 1/27.
So the simplified form of the expression 9^(-1/2) / 27^(2/3) is 1/27.
Therefore, the correct answer is (d) 1/27.