Question 27 (5 points)
Simplify: $\frac{\left(9 x^{6} y^{-8}\right)^{\frac{1}{2}}\left(2 x^{3} y\right)^{4}}{\left(\frac{1}{2} x^{-9} y^{6}\right)^{-2}}$. Your final answer must have positive exponents only. Show your work. Complete your solution on paper then upload a picture of your solution.

Step 1 ：First, we simplify the expression inside each parenthesis by applying the power of a power rule, which states that \((a^m)^n = a^{mn}\), and the product of powers rule, which states that \(a^m * a^n = a^{m+n}\).

Step 2 ：Next, we simplify the fraction by applying the quotient of powers rule, which states that \(a^m / a^n = a^{m-n}\).

Step 3 ：Finally, we simplify the expression to have positive exponents only. This involves applying the rule that \(a^{-n} = 1/a^n\).

Step 4 ：The expression has been simplified, but it still contains negative exponents. We need to further simplify it to have positive exponents only.

Step 5 ：The simplified expression with positive exponents only is \(\boxed{12y^{16}\sqrt{\frac{x^{6}}{y^{8}}}/x^{6}}\).