1.zapisz wyrażenie w najprostrzej postaci ; a)x^-3y^-2z^5/z^-2y^-3z^6 b)(x^-2y/z^3)^-3:(x^5y^-2/z^3)^-1 2.Wykonaj działanie; a)3^-2/2^5*2^4/3^-1 b)7^-1(7^2+7^0) c)1^-2+2^-2/(2/3)^-2+(-4)^-1*5+2^-2       /- to jest ułamek ^potęga

zad 1 a) [x⁻³y⁻²z⁵]/[z⁻²y⁻³z⁶]= =x⁻³y⁻²z⁵ * z²y³z⁻⁶= =x⁻³ * y⁻²⁺³ * z⁵⁺²⁻⁶= =x⁻³ * y¹ * z¹= =yz/x³ [Potęga trzecia dotyczy tylo niewiadomej x w mianowniku] --------------- b)  [latex](frac{x^{-2}y}{z^{3}})^{-3}:(frac{x^{5}y^{-2}}{z})^{-1}=(x^{-2}yz^{-3})^{-3}:(x^{5}y^{-2}z^{-1})^{-1}=\ =(x^{-2*(-3)}y^{1*(-3)}z^{-3*(-3)}):(x^{5*(-1)}y^{-2*(-1)}z^{-1*(-3)})=\ =(x^{6}y^{-3}z^{9}):(x^{-5}y^{2}z^{3})=x^{6}y^{-3}z^{9}*x^{5}y^{-2}z^{-3}=\ =x^{6+5}y^{-3-2}z^{9-3}=x^{11}y^{-5}z^{6}=frac{x^{11}z^{6}}{y^{5}}[/latex] ------------------------------------------ zad 2 a) 3⁻²/2⁵ * 2⁴/3⁻¹= =3⁻² * 2⁻⁵ * 2⁴ * 3¹= =3⁻²⁺¹ * 2⁻⁵⁺⁴= =3⁻¹ * 2⁻¹= =(3*2)⁻¹= =6⁻¹= =1/6 --------------- b) 7⁻¹(7²+7⁰)= =7⁻¹ * 7² + 7⁻¹ * 1= =7⁻¹⁺² + 7⁻¹= =7 + 1/7 =50/7 --------------- c) [1⁻²+2⁻²]/(2/3)⁻² + (-4)⁻¹ * 5+2⁻²= =[1 + 1/4] * (2/3)² + (-1/4) * 5 + 1/4= =5/4 * 4/9 + (-5/4) + 1/4 =5/9 -1= =-4/9