Question

Care din urm.puteri sunt pătrate perfecte?
27,2 la puterea 16, 3 la puterea 4, 81 la puterea 3 , 27la puterea 3 ,2la puterea 576,9la puterea 1967,9la puterea 2009 ,2 la puterea 2010,5 la puterea 2k , 8 la puterea 3k,4la puterea 5 k,unde k este nr natural .

Answer 1

27=3^3(^ este la puterea) deci nu e
2^16=2^8*2^8=(2^8)^2= deci e patrat perfect
3^4=3^2*3^2=9^2 patrat perfect
81^3=(3^4)^3=3^12=(3^6)^2 patrat perfect
2^576=(2^288)^2= patrat perfect
9^1967=3^(2*1967)=(3^1967)^2 patrat perfect
2^2010=(2^1005)^2= patrat perfect
5^2k=(5^k)^2 patrat perfect
8^3k=2^6k=(2^3k)^2 patrat perfect
4^5k=2^10k=(2^5)^2 patrat perfect