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1. Transformati puterile in radicali:
a) ( 1/2) la puterea 1/3
b) (2/5) la puterea 2/6
2. Transformati radicalii in puteri:
a) √5
b) ∛50
c) ∛125
d) 1/∛8/9
3. Transformati, dupa caz, radicalii in puteri si puterile in radicali:
a) ∛16 ; b) ∛75 ; c) ∛x la puterea 9 ; d) 1/√3 la puterea 4 ; e) (3/2) la puterea 3/2 ; f) [0,1(3)] la puterea 1/2


Răspuns :

1.
a)  rad3(1/2), a se citi si scrie radical de ordinul 3
b) 2/5^1/3=rad382/5)

2.
a) 5^1/2
b) 50^1/3
c (5x5x5)^1/3 = 5
d) 1 supra 2 x 3^2/3, pt ca rad3(8)=rad3(2^3)=2

3.
a) revin in cateva minute.......suna telefonul.........sory.
ok, am revenit
a) rad3(8x2)=2x(2)^1/3
b)rad3(75)=75^1/3
c)x^9/3= x^3
d) 1 supra 3^2 = 3^-2
e) (3/2)^3/2 = 3/2rad(3/2)
f) rad(13-1 supra 90)= rad(12/90) =2rad3 supra 3rad10

Mult succes!
exe 1
2 ^ (-1/3), radical indice 3 din 1/2=∛(1/2)
2/5^(1/3)=∛(2/5)=∛0,4

exe 2.
 5 ^ (1/2)
50 ^ (1/3)
c) 5=5^1
d)1/2/3=3/2 = (3/2) ^1

exe 3.
a)2^ (4/3)
b). 75 ^ (1/3)
c) x^ (9/3)=x³
c) 3 ^ (-4/2) =3^ (-2)
d) 3√3/ (2√2)
e)√(1/6)=1/√6=(√6)/6