Question

2 gimnazjum :)

potęgowanie ilorazu i iloczynu

Oblicz sprytnie:
a)4^5*5^6
b) (3/5)^5*(5/3)^6
c) (4/9)^7*(2/9)^8
d) (1 4/9)^5:(4 1/3)^4

Answer 1

potęgowanie ilorazu i iloczynu

Oblicz sprytnie:
a)4^5*5^6 =

= 4⁵ *5⁶ =

= (2²)⁵ *5⁶ =

= 2¹⁰ * 5⁶=

= 2⁴*2⁶*5⁶ =

= 2⁴*(2*5)⁶ =

= 2⁴*10⁶ =

= 16*1 000 000 =

= 16 000 000

b) (3/5)^5*(5/3)^6 =

= (3/5)⁵ *( 3/5)⁻⁶ =

= (3/5)¹ =

= 5/3

c) (4/9)^7*(2/9)^8=

= (2)⁷*(2/9)⁷ *(2/9)⁸ =

= 2⁷*(2/9)¹⁵=

= 2²² / 9¹⁵

d) (1 4/9)^5:(4 1/3)^4 =

= (13/9)⁵ :  (13/3)⁴ =

= (1/3)⁵*(13/3)⁵ : (13/3)⁴ =

= (1/3)⁵* (13/3)¹ =

= (1/3)⁵*(1/3)¹ *13 =

= 13* (1/3)⁶=

= 13*(1/729) =

= 13/729