Question

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oblicz sprytnie
a) 4 do potengi 5 * 5 do 6
b) (3/5) do 5 * (5/3 ) do 6
c) ( 4/9 )do 7 : ( 2/9) do 8
d) ( 1 i 4/9 ) do 5 : ( 4 i 1/3 ) do 4

Answer 1

A) 4 do potęgi 5 * 5 do 6= 1024 * 15625=16000 000
b) (3/5) do 5 * (5/3 ) do 6= 1 2/3
c) ( 4/9 )do 7 : ( 2/9) do 8=(2²)⁷/9⁷ * 9⁸/2⁸ = 2¹⁴/9⁷ * 9⁸/2⁸= 64 * 9 = 576
d) ( 1 i 4/9 ) do 5 : ( 4 i 1/3 ) do 4=
(1 i4/9)⁵ : (4i 1/3)⁴ = (13/9)⁵ : (13/3)⁵ = 13⁵/9⁵ : 13⁵/3⁵ = 13⁵/(3²)⁵ * 3⁵/13⁵ = 13⁵/3¹⁰ * 3⁵/13⁵ = 1/3⁵ = 1/243

Answer 2

A) 4 do potęgi 5 * 5 do 6
4⁵ * 5⁶ = 4⁵ * 5⁵ * 5¹ = (4*5)⁵ * 5 = 20⁵ * 5 = (2*10)⁵ * 5 = 2⁵ * 10⁵ * 5 = 32 * 5 * 10⁵ = 160 * 10⁵ = 160 * 10000 = 16000000

b) (3/5) do 5 * (5/3 ) do 6
(³/₅)⁵ * (⁵/₃)⁶ = 3⁵/5⁵ * 5⁶/3⁶ = ⁵/₃ = 1⅔

c) ( 4/9 )do 7 : ( 2/9) do 8
(⁴/₉)⁷ : (²/₉)⁸ = 4⁷/9⁷ : 2⁸/9⁸ = (2²)⁷/9⁷ * 9⁸/2⁸ = 2¹⁴/9⁷ * 9⁸/2⁸ = 2⁶ * 9 = 64 * 9 = 576

d) ( 1 i 4/9 ) do 5 : ( 4 i 1/3 ) do 4
(1⁴/₉)⁵ : (4⅓)⁴ = (¹³/₉)⁵ : (¹³/₃)⁵ = 13⁵/9⁵ : 13⁵/3⁵ = 13⁵/(3²)⁵ * 3⁵/13⁵ = 13⁵/3¹⁰ * 3⁵/13⁵ = 1/3⁵ = ¹/₂₄₃