Question

scrie rezultatul sub forma de puteri a) (13/25)⁵¹•(13/25)⁴•(13/25) b)(7/8)¹⁵:(7/8)³ c)(13/36)⁵×(9/26)⁵ d)(27/12)³⁵:(9/24)³⁵ e){[(1/21)⁰]²⁰}²⁰²¹ f)(8/11)¹×(8/11)²×(8/11)³×.......(8/11)⁸×(8/11)⁹×(8/11)¹⁰ g)(3/4)¹¹×(4/5)¹²×(5/6)¹²......(10/11)¹²×(11/12)¹²×(12/13)¹²​

Answer 1

Răspuns:

Explicație pas cu pas:

a) (13/25)⁵¹•(13/25)⁴•(13/25) = (13/25)⁵¹⁺⁴⁺¹ = (13/25)⁵⁶

b) (7/8)¹⁵:(7/8)³ = (7/8)¹⁵⁻³ = (7/8)¹²

c) (13/36)⁵×(9/26)⁵ = (13·9/36·26)⁵ = (1/8)⁵

d) (27/12)³⁵:(9/24)³⁵ = (27/12 ·24/9)³⁵ = (27·24/12·9) ³⁵ = 6³⁵

e) {[(1/21)⁰]²⁰}²⁰²¹ = 1²⁰ˣ²⁰²¹ = 1

f) (8/11)¹×(8/11)²×(8/11)³×.......(8/11)⁸×(8/11)⁹×(8/11)¹⁰ =

=(8/11)¹⁺²⁺······⁺¹⁰ = (8/11)⁽¹¹ˣ¹⁰⁾/² = (8/11)⁵⁵

g) (3/4)¹¹×(4/5)¹²×(5/6)¹²......(10/11)¹²×(11/12)¹²×(12/13)¹²​ =

= (3/4)¹¹ ·(4/5 ·5/6 · .......·10/11 ·11/12 ·12/13)¹² =

= (3/4)¹¹ ·[(4·5·6·.....·10·11·12)/(5·6·....·11·12·13)]¹² =

= (3/4)¹¹· (4/13)¹² = (3¹¹·4¹²):(4¹¹·13¹²) = (3¹¹·4)/13¹²