Question

Arătați ca urmatoarele numere naturale sunt cuburi perfecte:
a)3^69
b)4^51
c)8^61
d)5^21
e)19^33
f)17^42
g)27^28
h)64^23

Answer 1

a)3^69 = 3^(23×3) = (3^23)^3

b)4^51 = 4^(17×3) = (4^17)^3

c)8^61 = (2^3)^61 = (2^61)^3

d)5^21 = 5^(7×3) = (5^7)^3

e)19^33 = 19^(11×3) = (19^11)^3

f)17^42 = 17^(14×3) = (17^14)^3

g)27^28 = (3^3)^28 = (3^28)^3

h)64^23 = (4^3)^23 = (4^23)^3