Arătați că următoarele numere sunt pătrate perfecte ​

c) 625^7 = (5^4)^7 = 5^28 = (5^14)^2

d) 9^27 = (3^2)^27 = 3^54 = (3^27)^2

e) 121^121 = (11^2)^121 = 11^242 = (11^121)^2

f) (2×8)^17 = (2×2^3)^17 = (2^4)^17 = 2^68 = (2^34)^2

g) 32^19 : 2^19 = (2^5)^19 : 2^19 = 2^95 : 2^19 = 2^76 = (2^38)^2

h) 81^12 = (3^4)^12 = 3^48 = (3^24)^2

Răspuns:

Explicație pas cu pas:

a)  625⁷ = ( 5⁴)⁷ = 5⁴ˣ⁷ = 5⁷ˣ²ˣ² = (7¹⁴)² ->  patrat perfect

d)  9²⁷ = ( 3²)²⁷ = ( 3²⁷)² -> p.p.

e)  121¹²¹ = ( 11²)¹²¹ = 11¹²¹ˣ² = ( 11¹²¹)² ->  p.p

f)  ( 2 x 8 )¹⁷ = ( 16)¹⁷ = ( 4²)¹⁷ = ( 4¹⁷)² -> p.p

g)  32¹⁹ : 2¹⁹ = ( 32 : 2)¹⁹ = 16¹⁹ = ( 4²)¹⁹ = ( 4¹⁹)² -> p.p.

h)   81¹²⁹ = ( 9²)¹²⁹ =9²ˣ¹²⁹ =  ( 9¹²⁹)² -> patrat perfect