Question

Oblicz, stosując prawa działań na potęgach:
a) (1 1/5)^5 * ( 1 2/3)^5 , (1 4/5)^4 : (0,6)^4 , (18 pierwiastek z 5 )^2 : (6 pierwiastek z 5)^2 b) 2^-3 , (2/5)^-2 , (0,2)^-3 , (4 1/5)^1
c) 4^-2 *(1/16)^2 , (1 1/6)^-3 * (3/7)^-3

Answer 1

a)  (1⅕)⁵· (1⅔)⁵ = (1⅕ · 1⅔)⁵ = (⁶/₅ · ⁵/₃ )⁵ = 2⁵ = 32

 

      (1⅘)⁴ : (0,6)⁴ = (1,8)⁴ : (0,6)⁴ = (1,8 : 0,6)⁴ = (18:6)⁴ = 3⁴ = 81

     

      (18√5)² : (6√5)² =( 18√5 : 6√5) ² = 3² = 9

 

b)  2⁻³ = (½)³ =⅛

     (⅖)⁻² = (⁵/₂)² = ²⁵/₄ = 6¼

     (0,2)⁻³ = (⅕)⁻³ = 5³ = 125

     (4⅕)¹ = 4⅕,            (4⅕)⁻¹ = (²¹/₅)⁻¹ = (⁵/₂₁)¹ =⁵/₂₁

c)

     4⁻² · ( ¹/₁₆)² = (¼)² · (¹/₁₆)² = (¼ · ¹/₁₆)² = (¹/₆₄)² = ¹ /₄₀₉₆

    4⁻² · (¹/₁₆)⁻² = (4· ¹/₁₆)⁻² = 4⁻² = (¼)² = ¹/₁₆

   

    (1⅙)⁻³ · (³/₇)⁻³ = ( ⁷/₆ · ³/₇ ) ⁻³ = (½)⁻³ = 2³ = 8