Question

e) 9:31: 6. Scrieți sub forma unei singure puteri cu exponent număr natural:
a) 25¹⁰×5³²×125⁵=..........
b) 9⁴×27⁵×3¹⁴=.................
c) 2¹⁵×4¹²×8⁶=...................​

Answer 1

Răspuns:

a)

25^10 x 5^32 x 125^5 =  

(5^2)^10 x 5^32 x (5^3)^5 =

5^(2x10) x 5^32 x 5^(3x5) =  

5^20 x 5^32 x 5^15 =  

5^(20+32+15) =

5^67  

b)

9^4 x 27^5 x 3^14 =

(3^2)^4 x (3^3)^5 x 3^14 =

3^(2x4) x 2^(3x5) x 3^14  

3^8 x 3^15 x 3^14 =  

3^(8+15+14) =

3^37  

c)

2^15 x 4^12 x 8^6 =  

2^15 x (2^2)^12 x (2^3)^6 =

2^15 x 2^(2x12) x 2^(3x6) =  

2^15 x 2^24 x 2^18 =  

2^(15+24+18) =  

2^57