To simplify the expression convert the mixed numbers into improper fractions:
(1 9/16)^(-1/2) x (1 3/5)^(-1) / 16^(1/2)
First, simplify the exponents:
(1 9/16)^(-1/2) = (25/16)^(-1/2)
(1 3/5)^(-1) = (8/5)^(-1)
16^(1/2) = √16 = 4
Now, calculate the values:
(25/16)^(-1/2) = (16/25)^(1/2) = √(16/25) = 4/5
(8/5)^(-1) = (5/8)^1 = 5/8
substitute the values back into the expression:
(4/5) x (5/8) / 4
Next, simplify the expression:
(4/5) x (5/8) = (4 x 5) / (5 x 8) = 20/40 = 1/2
Finally, divide by 4:
(1/2) / 4 = 1/2 x 1/4 = 1/8
Therefore, the simplified expression is 1/8.