Question

56.Oblicz

a) (3^7 * 3^-9) : 3^-6

b) (2^3 - 2^2 * 2^0) * 0,25^-4

c) ( (√5)^4 - 5^3) : 0,01^-2

d) 4^-10 * (8^3 - 2^9)

e) (18^-2 - 12^-3) * 36^3

f) 6^6 * (8^0 - 4)^-6

57.Zapisz w postaci x^k

a) x^4 * x^6 / x^3 * x^-5

b) (x^5 * x^-2)^3 : (x^-6 / x^-1)^-2

Answer 1

a/ (3⁷·3-⁹):3-⁶= 3⁷-⁹+⁶=3⁴

 

b/ ( 2³-2²·2⁰)·0,25-⁴= (2³-2²+⁰)·0,25-⁴=(8-4)·0,25-⁴=4·(1/4)-⁴=4·4⁴=4¹+⁴=4⁵

 

c/  (√5⁴-5³):0,01-²= (5⁴/²-5³):100²=(5²-5³):100²=(25-75):10000=-50:10000= -1/200=-200-¹

 

d/  4-¹⁰·(8³-2⁹)= 2-²⁰ (2⁶-2⁹)= 2-²⁰·2⁶ - 2-²⁰·2⁹= 2-¹⁴ -2-¹¹= 2-¹¹(2-³-1)=2-¹¹(1/8-8/8)=

      -7/8·2-¹¹

 

e/ (18-²-12-³)·36³=18-²·36³-12-³·36³= 18-²·(2·18)³-12-³(3·12)³=18-²·18³·2³-12-³·12³·3³=18¹·2³-12⁰·3³=18·8-1·27=144-27=117

 

f/ 6⁶(8⁰-4)-⁶=6⁶(1-4)-⁶=6⁶·(-3)-⁶=[(-2)·(-3)]⁶·(-3)-⁶=(-2)⁶·(-3)⁶·(-3)-⁶=(-2)⁶·(-3)⁰=(-2)⁶·1=(-2)⁶

 

57. a/    x⁴·x⁶/x³·x-⁵= x¹⁰/x-²=x¹²

      b/    (x⁵·x-²)³:(x-⁶/x-¹)-²= (x³)³:(x-⁵)-²= x⁹:x¹⁰= x-¹