Question

27⁹×32¹¹÷2-16⁶×2×6²⁷=p.p.

Answer 1

$27^9\times 32^{11}\div 2-16^6\times 2\times 6^{27}=\\ \\ = (3^3)^9\times (2^5)^{11}\div 2 - (2^4)^{6}\times 2\times (2\times 3)^{27}\\ \\ = 3^{27}\times 2^{55}\div 2-2^{24}\times 2\times 2^{27}\times 3^{27}\\ \\ = 3^{27}\times 2^{55-1}-2^{24+1+27}\times 3^{27}\\ \\ = 3^{27}\times 2^{54}-2^{52}\times 3^{27}\\ \\ = 3^{27}\times 2^{52}\times (2^2-1)\\ \\ = 3^{27}\times 2^{52}\times 3\\ \\ = 3^{28}\times 2^{52}\\ \\ = (3^{14}\times 2^{26})^{2}\to p.p.$