Question

aratati ca numarul n=27 la puterea9x32la puterea11:2-16la puterea6x2x6 la puterea27 este patrat perfect

Answer 1

n=27^9x32^11:2-16^6x2x6^27

n=(3^3)^9x(2^5)^11:2-(2^4)^6x2x(2x3)27

n=3^27x2^55:2-2^24x2x2^27x3^27

n=3^27x2^54-2^(24+1+27)x3^27

n=3^27x2^54-2^52x3^27

n=3^27x2^52(2^2-1)

n=3^27x2^52x3

n=2^52x3^28

n=(2^26x3^14)^2 este p.p.