Answer:
4096
Step-by-step explanation:
Lets start by applying a basic exponent rule. (a*b)^n is equal to a^n * b^n
Therefore,
((9(3/16)^-2)^3/2 = 9^3/2 * ((3/16)^-2)^3/2
Now lets focus on ((3/16)^-2)^3/2
(3/16)^-2 = 1/(3/16)^2 = (16^2/3^2)^3/2.
We can quickly eliminate the fractional exponent by plugging it into the numerator and the denominator and we get, 16^3/3^3 = 4096/27
So now we have, 9^3/2 * 4096/27
We can easily compute 9^3/2, which is (sqrt(9))^3, which is equal to 27.
Therefore, you have, 27*4096/27. The 27 cancels to give us a final answer of 4096
