Question

Scrieti rezultatul sub forma unei singure puteri:
A. (35/95)^6 x (38/14)^6
B. (33/50)^9 x (25/22)^9
C. (3/7)^4 x (49/36 )^4 x (49/36)^2
D. (7/17)^5 : (21/17)^5
E. (13/8)^6 : (39/32)^6
Ajutor plzz ;^;
Dau coroana + 30 puncte

Answer 1

Răspuns:

Explicație pas cu pas:

a)  (35/95)⁶ x ( 38/14)⁶ = [(7/19)x(19/7)]⁶ = 1⁶ = 1

35/95 =(35:5)/(95:5)=7/19 -> am simplificat fractia 35/95 cu 5

38/14 =(38:2)/(14:2) = 19/7 -> am simplificat fractia initiala cu 2

-> pentru ca sunt puteri cu acelasi exponent, se scriu bazele in produs, la acelasi exponent

-> observam ca se simplifica 7/7, dar si 19/19 rezultand produsul 1

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b)

(33/50)⁹ x (25/22)⁹ = [(33/22)x(25/50)]⁹ = (3/4)⁹

33/22 =(33:11)/(22:11)=3/2 -> simplific cu 11

25/50 = (25:25)/(50:25) = 1/2 -> simplific cu 25

(3/2) x ( 1/2) = 3/(2x2) = 3/4

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c)

(3/7)⁴x (49/36)⁴ x (49/36)² =

= [(3/36) x ( 49/7)]⁴ x (7²/6²)² =

= (7/12)⁴ x ( 7/6)²ˣ² =

= [ (7x7)/(12x6)]⁴ =

= (49/72)⁴

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d)

(7/17)⁵ : (21/17)⁵ = (7/17)⁵ x (17/21)⁵ = [ (7/21) x (17/17)]⁵ = (1/3)⁵

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e)

(13/8)⁶ : (39/32)⁶ =[ (13/8) x (32/39)]⁶ = [ (13/39) x(32/8)]⁶ = (4/3)⁶