Hej!
Od a) do c) :
[tex]a] \ (6^3)^4\cdot(6^2)^3=6^{12}\cdot6^6=6^{18}\\\\b] \ (7^2)^5\cdot(7^5)^2=7^{10}\cdot7^{10}=7^{20}\\\\c] \ ((\frac{1}{3})^3)^3\cdot((\frac{1}{3})^2)^2=(\frac{1}{3})^9\cdot(\frac{1}{3})^4=(\frac{1}{3})^{13}[/tex]
Od d) do f) :
[tex]d] \ (5^8)^7:(5^6)^8=5^{56}:5^{48}=5^8\\\\e] \ (0,6^4)^5:(0,6^7)^2=0,6^{20}:0,6^{14}=0,6^6\\\\f] \ ((\frac{5}{7})^3)^8:((\frac{5}{7})^2)^{10}=(\frac{5}{7})^{24}:(\frac{5}{7})^{20}=(\frac{5}{7})^4[/tex]
Użyłam wzorów :
[tex]a^m\cdot a^n=a^{m+n}\\\\a^m:a^n=a^{m-n}[/tex]
Odpowiedź:
a) (6³)⁴ * (6²)³ = 6³ˣ⁴ * 6²ˣ³ = 6¹² * 6⁶ = 6¹²⁺⁶ = 6¹⁸
b) (7²)⁵ * (7⁵)² = 7²ˣ⁵ * 7⁵ˣ² = 7¹⁰ * 7¹⁰ = 7¹⁰⁺¹⁰ = 7²⁰
c) ((1/3³)³ * ((1/3)²)² = (1/3)³ˣ³ * (1/3)²ˣ² = (1/3)⁹ * (1/3)⁴= (1/3)¹³
d) (5⁸)⁷ : (5⁶)⁸ = 5⁸ˣ⁷ : 5⁶ˣ⁸ = 5⁵⁶ : 5⁴⁸ = 5⁵⁶⁻⁴⁸ = 5⁸
e) (0,6⁴)⁵ : (0,6⁷)² = (0,6)⁴ˣ⁵ ; (0,6)⁷ˣ² = (0,6)²⁰ : (0,6)¹⁴ = 0,6²⁰⁻¹⁴= 0,6⁶
f) ((5/7)³)⁸ : ((5/7²)¹⁰ = (5/7)³ˣ⁸ : (5/7)²ˣ¹⁰ = (5/7)²⁴ : (5/7)²⁰ = (5/7)⁴