Potegi i pierwiastki.   zadania w załączniku. błagam o pomoc.

Zad. 10 (⅕)³* 125⁻⁴ * 25² = 5⁻³ * (5³)⁻⁴ * (5²)² = 5⁻³ * 5⁻¹² * 5⁴ = 5⁻¹⁵ * 5⁴ = 5⁻¹¹ Zad. 11 licznik: 0,25² * ½ * 32⁻³=(¼)² * ½ * (1/32)³=((½)²)² * ½ * ((½)⁵)³=(½)⁴ * ½ * (½)¹⁵=(½)²⁰ mianownik: (1/16)⁻¹ * 0,5³ * (⅛)⁴ = ((½)⁴)⁻¹ * (½)³ * ((½)³)⁴ = (½)⁻⁴ * (½)³ * (½)¹² = (½)¹¹ otrzymujemy: (½)²⁰ ÷ (½)¹¹ = (½)⁹ = 1/512 Zad. 12 licznik: a⁵ * a⁻³ ÷ (a²)⁻⁷ * a⁻¹⁴ = a² ÷ a⁻¹⁴ * a⁻¹⁴ = a¹⁶ * a⁻¹⁴= a² mianownik: (a⁻³)⁻⁴ ÷ (a⁷)⁻¹ * a⁻¹⁷ = a¹² ÷ a⁻⁷ * a⁻¹⁷ = a¹⁹ * a⁻¹⁷= a² otrzymujemy: a²÷a² = 1 Zad. 13 a) √18 + 4√2 = √(2*9) + 4√2 = 3√2 + 4√2 = 7√2 b) 3√24 + 2√54 - √150 = 3√(4*6) + 2√(9*6) - √(25*6) = 3*2√6 + 2*3√6 - 5√6 = 6√6 + 6√6 - 5√6 = 7√6 Zad. 14 a) 5/√3 *√3/√3 = 5√3/3 b) 5/(√2 + 1) * (√2 - 1)/(√2 - 1) = 5(√2 - 1)/(2-1) = (5√2 - 5)/1 = 5√2 - 5 c) (1+√3)/(3-√5) * (3+√5)/(3+√5) = (1+√3)(3+√5)/(9-5)= (3+√5+3√3+√15)/4  

10. (1/5)^3 x125^-4 x 25^2 = 5^-3 x (5^3)^-4 x (5^2)^2 = =5^-3 x 5^-12 x5^4 =5^-15 x5^4 =5^-11 11. (0,25)^2 x 1/2 x 32^-3)/[(1/16)^-1 x 0,5^3 x (1/8)^4 = =[(1/2)^4 x1/2 x(1/2)^15]/[(1/2)^-4 x (1/2)^3 x(1/2)^12 = = (1/2)^20/(1/2)^11 = (1/2)^9 12. [(a^5 x a^-3):(a^2)^-7 x a^-14] : [(a^-3)^-4 : (a^7)^-1 xa^-17] = =(a^2 : a^-14 x a^-14) : (a^12 : a^-7 x a^-17) =(a^16 xa^-14):(a^19 x a^-17)= = a^2 : a^2 =1 13. a) V18 + 4V2 =3V2 + 4V2 =7V2 b) 3V24 +2V54 -V150 =6V6 +6V6 -5V6 =7V6 14. a) 5/V3 =5/V3 xV3/V3 =5V3/3 b) 5/(V2 +1) =5/(V2 +1) x( V2 -1)/(V2-1) =5(V2-1) c) (1 +V3)/(3 -V5) =(1 +V3)/(3-V5) x (3+V5)/(3 +V5) =(1 +V3)(3 +V5)/4