\( \sqrt {\sqrt [3]{79}.}\frac{\pi }{2}\div (2^{2})^{9^{2^{\pi .85^{2}}}}= \)

Let's break this down step by step! Starting from the left, you have \(\sqrt{\sqrt[3]{79}}\) which gives us \(79^{1/6}\). Next, you have \(\frac{\pi}{2}\). Then, you have \(2^{2}\) raised to the \(9^{2^{\pi \cdot 85^{2}}}\). Calculating \(2^2\) gives you 4, so \(4^{9^{2^{\pi \cdot 85^{2}}}}\) becomes quite a massive number. Now combining these should yield a complex expression. However, if simplifying is your goal, it’s often helpful to look for cancellation. The terms can get unwieldy fast! A calculator or computer algebra system might be your best bet for the final evaluation, as the exponent will likely result in a very large number. Happy calculating!