Question

zad. 3, 4, 5

Answer 1

Zad. 3)

 

a)

 

x = (27⁹ + 81⁷) :  9¹³

 

x = [(3³)⁹ + (3⁴)⁷] : (3²)¹³

 

x = (3²⁷ + 3²⁸) : 3²⁶

 

x = 3²⁶(3 + 3²) : 3²⁶

 

x = 3 + 9

 

x = 12

 

y = (8¹⁶ + 4²⁵) :(5 x 16¹²)

 

y = [(2³)¹⁶ + (2²)²⁵] : [5 x (2⁴)¹²]

 

y = (2⁴⁸ + 2⁵⁰) : (5 x 2⁴⁸)

 

y = ( 2⁴⁸ + 2⁴⁸ x 2²) : (5 x 2⁴⁸)

 

y = 2⁴⁸ x ( 1 + 2²) : (5 x 2⁴⁸)

 

y = 2⁴⁸ x ( 1 + 4) : (5 x 2⁴⁸)

 

y = (2⁴⁸ x 5) : (5 x 2⁴⁸)

 

y = 1

 

(x/y) * 100%

 

(12/1) * 100%

 

1200%

 

b)

 

x = (5⁻²⁰ + 5⁻¹⁹) : 125⁻⁶

 

x = (5⁻¹⁹ x 5⁻¹ + 5⁻¹⁹) : (5³)⁻⁶

 

x = 5⁻¹⁹ x (5⁻¹ + 1) : 5⁻¹⁸

 

x = 5⁻¹ x 1,2

 

x = 0,2 x 1,2

 

x = 0,24

 

y = [6⁻¹⁴ + 12 x (1/6)¹⁵] : [0,5¹⁴ x (1/3)¹⁵]

 

y = (6⁻¹⁴ + 12 x 6⁻¹⁵) : (0,5¹⁴ x 3⁻¹⁵)

 

y = 6⁻¹⁴ x (12 x 1/6) : (0,5¹⁴ x 3⁻¹⁵)

 

y = (6⁻¹⁴ x 2) : (0,5¹⁴ x 3⁻¹⁵)

 

y = (6⁻¹⁴ x 2) : (2⁻¹⁴ x 3⁻¹⁴ x 3⁻¹)

 

y = (6⁻¹⁴ x 2) : (6⁻¹⁴ x 3⁻¹)

 

y = 2 : (1/3)

 

y = 6

 

(0,24/6) * 100% = 0,04 * 100% = 4%

 

Zad. 4)

 

a)

 

(2/3 - 2⁻²)⁻¹ = (2/3 - 1/4)⁻¹ =

 

= (8/12 - 3/12)⁻¹ =

 

= (5/12)⁻¹ =

 

= 12/5 =

 

= 2,4

 

b)

 

[∛8⁻¹ - "pierw4st"(9⁻²)]⁻¹ = (0,5 - 1/3)⁻¹ =

 

= (3/6 - 2/6)⁻¹ =

 

= (4/6)⁻¹ =

 

= (2/3)⁻¹ =

 

= 3/2 =

 

= 1,5

 

c)

 

[(3/4)⁻¹ - (1,5)⁻¹]⁻² = (4/3 - 2/3)⁻² =

 

= (2/3)⁻² =

 

= 9/4 =

 

= 2,25

 

d)

 

[(1,25)⁻¹ - ∛8/27]⁻² = (0,8 - 2/3)⁻² =

 

= (4/5 - 2/3)⁻² =

 

= (12/15 - 10/15)⁻² =

 

= (2/15)⁻² =

 

= 225/4 =

 

= 56,25

 

Zad. 5)

 

a)

 

√9 x [(1,5)⁻¹ + 9^(- 1,5)] x 27^(2/3) = 3 x (2/3 + 1/27) x 1/9 =

 

= 1/3 x (18/27 + 1/27) =

 

= 1/3 x 19/27 =

 

= 19/81

 

b)

 

[(81/625)^( - 0,75) : (5/3)³ - (0,125)^(1/3)]⁻² = [(5/3)³ : (5/3)³ - 0,5]⁻² =

 

= (1 - 0,5)⁻² =

 

= 0,5⁻² =

 

= 4

 

c)

 

∛0,375 x ∛9 + (3⁻¹ - "pierw4st"16/81)⁻² = (∛3,375 + 2/3)⁻² =

 

= (∛27/8 + 2/3)⁻² =

 

= (3/2 + 2/3)⁻² =

 

= (9/6 + 4/6)⁻² =

 

= (10/6)⁻² =

 

= (5/3)⁻² =

 

= 9/25 =

 

= 0,36