Question

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

Answer 1

n = 27^9 × 32^11 : 2 - 16^6×2×6^27

n = (3^3)^9×(2^5)^11:2-(2^4)^6×2×6^27

n = 3^27×2^55:2 - 2^24 × 2 × 6^27

n = 3^27 × 2^54 - 2^25 × 3^27 × 2^27

n = 3^27 × 2^54 - 2^52 × 3^27

n = 3^27 × 2^52 × ( 2^2 - 1)

n = 3^27 × 2^52 × 3

n = 3^28 × 2^52

n =( 3^14)^2 × (2^26)^2

n = (3^14 × 2^26)^2 p.p