Question

Scrieti sub forma de puteri care au aceeasi baza:
e) $[0,1(3)]^{3}$ si $\frac{4}{225}$

Scrieti ca puteri care au acelasi exponent:
a) $(\frac{1}{3})^{26}$ si $(\frac{1}{4})^{39}$
c) $[1,(7)]^{75}$ si $[4,(629)]^{50}$
d) $(10,5)^{27} si (\frac{23}{5})^{54}$

Answer 1

Scrieti sub forma de puteri care au aceeasi baza:
 e) [0,1(3)]^3 =[(13-1)/90]^3=(12/90)^3=(4/30)^3
4/225=0,01(7)=(17-1)/900=16/900=(4/30)^2


Scrieti ca puteri care au acelasi exponent:
a) (1/3)^26 =[(1/3)^2]^13=(1/9)^13
   (1/4)^39=[(1/4)^3]^13=(1/64)^13
 c)  [1,(7)]^75= [(16/9)^3]^25=(4096/729)^25
1,(7)=(17-1)/9=16/9
     [4,(629)]^50=[(4625/999)^2]^25=(21390625/99801)^25
4,(629)=(4629-4)/9=4625/999

d) (10,5)^27
(23/5)^54=[(23/5)^2]^27=(529/25)^27