Question

Find the value of the following expression:

Answer 1

$\bf \left( 3^8\cdot 2^{-5}\cdot 9^0 \right)^{-2}\cdot \left( \cfrac{2^{-2}}{3^3}\right)^{-4}\cdot 3^{28} \\\\\\ \left( 3^8\cdot \cfrac{1}{2^5}\cdot 1 \right)^{-2}\cdot \left( \cfrac{3^3}{2^{-2}}\right)^{4}\cdot 3^{28}\implies \left( \cfrac{3^8}{2^5}\right)^{-2}\cdot \left( \cfrac{3^3\cdot 2^2}{1}\right)^{4}\cdot 3^{28}$

$\bf \left( \cfrac{2^5}{3^8}\right)^{2}\cdot \left( \cfrac{3^3\cdot 2^2}{1}\right)^{4}\cdot 3^{28}\implies \left( \cfrac{2^{5\cdot 2}}{3^{8\cdot 2}} \right)\left( 3^{3\cdot 4}\cdot 2^{2\cdot 4} \right)\cdot 3^{28} \\\\\\ \cfrac{2^{10}}{3^{16}}\cdot 3^{12}\cdot 3^{28}\cdot 2^8\implies \cfrac{2^{10}\cdot 2^8\cdot 3^{12}\cdot 3^{28}}{3^{16}}\\\\\\ 2^{10}\cdot 2^8\cdot 3^{12}\cdot 3^{28}\cdot 3^{-16}$

$\bf 2^{10+8}\cdot 3^{12+28-16}\implies 2^{18}\cdot 3^{24}\implies 262144\cdot 282429536481 \\\\\\ 74037208411275264$