Question

Oblicz:

a) [(½)³]⁻³ :16²=

b) (1/64)⁻³ * 8⁻³/2⁵=

c) 25⁻²/5⁻⁴ - (3/5)⁻⁶ * (5/3)⁻⁷=

d) [(9/7)⁻³ : (3/7)⁻³] * (⅓)⁻⁶=

e) (125/16)⁻² : (75/8)⁻³=

f) (54/35)³ * (81/49)⁻² * (5/6)³=

Answer 1

a]

[(½)³]⁻³:16²=(½)⁻⁹:(2⁴)²=2⁹;2⁸=2

b]

(1/64)⁻³×8⁻³/2⁵=(2⁻⁶)⁻³×(2³)⁻³:2⁵=2¹⁸×2⁻⁹;2⁵=2⁴=16

c]

25⁻²/5⁻⁴-(⅗)⁻⁶×(⁵/₃)⁻⁷=(5²)⁻²/5⁻⁴-(⅗)⁻⁶×(⅗)⁷=1-(⅗)¹=⅖

d]

[(9/7)⁻³:(3/7)⁻³]×(⅓)⁻⁶=3⁻³×3⁶=3³=27

e]

(125/16)⁻²:(75/8)⁻³=(16/125)²:(8/75)³=256/15625:512/421875=27/2=13,5

f]

(54/35)³×(81/49)⁻²×(⅚)³=(270/210)³×(7/9)⁴=(9/7)³×(9/7)⁻⁴=7/9

Answer 2

a) [(½)³]⁻³ :16²= (1/2)^-9 : (2^4)^2 = 2^9 : 2^8 = 2^1 = 2

b) (1/64)⁻³ * 8⁻³/2⁵= 64^3 * 8^-3 : 2^5 = (2^6)^3 * (2^3)^-3 : 2^5 = 2^18 * 2^-9 : 2^5 = 2^9 : 2^5 = 2^4 = 16

c) 25⁻²/5⁻⁴ - (3/5)⁻⁶ * (5/3)⁻⁷= (5^2)^-2 : 5^-4 - (5/3)^6 * (5/3)^-7 = 5^-4 : 5^-4 - (5/3)^-1 = 5^0 - 3/5 = 1 - 3/5 = 2/5

d) [(9/7)⁻³ : (3/7)⁻³] * (⅓)⁻⁶= (9/7 : 3/7)^-3 * (1/3)^-6 = (9/7 * 7/3)^-3 * (1/3)^-6 = 3^-3 * (1/3)^-6 = (1/3)^3 * (1/3)^-6 = (1/3)^-3 = 3^3 = 27

e) (125/16)⁻² : (25/8)⁻³= (5^3)^-2 : (2^4)^-2 : (5^2)^-3 : (2^3)^-3 = 5^-6 : 2^-8 : 5^-6  : 2^-9 = 5^0 : 2^1 = 1 : 2 = 1/2

f) (54/35)³ * (81/49)⁻² * (5/6)³= (54/35 * 5/6)^3 * (81/49)^-2 = (9/7)^3 * {(9/7)^2}^-2 = (9/7)^3 * (9/7)^-4 = (9/4)^-1 = 4/9