Zadanie 4. Oblicz:
a)
\frac{1}{2}*[(-1)^8+(-1)^8]=\frac{1}{2}*(1+1)=\frac{1}{2}*2=1
b)
(-3\frac{1}{3})^3*0,3^4-(-\frac{1}{2})^3*(1\frac{1}{3})^3=(-\frac{10}{3})^3*(\frac{3}{10})^4-(-\frac{1}{2^3})*(\frac{4}{3})^2=-\frac{10^3}{3^3}*\frac{3^4}{10^4}+\frac{1}{8}*\frac{16}{9}=-10^{3-4}*3^{4-3}+\frac{2}{9}=-10^{-1}*3+\frac{2}{9}=-\frac{1}{10}*3+\frac{2}{9}=-\frac{3}{10}+\frac{2}{9}=-\frac{27}{90}+\frac{20}{90}=-\frac{7}{90}
c)
(1\frac{1}{3})^3*(-3\frac{3}{4})^2:3-(\frac{1}{3})^2=(\frac{4}{3})^3*(-\frac{15}{4})^2:3-\frac{1}{9}=\frac{64}{27}*\frac{225}{16}:3-\frac{1}{9}=\frac{4}{3}*25:3-\frac{1}{9}=\frac{100}{3*3}-\frac{1}{9}=\frac{100}{9}-\frac{1}{9}=\frac{99}{9}=11
d)
(-0,3)^2:0,1-0,2^3*(2\frac{1}{2})^2=(-\frac{3}{10})^2:\frac{1}{10}-0,008*(\frac{5}{2})^2=
\frac{9}{100}*\frac{10}{1}-\frac{8}{1000}*\frac{25}{4}=\frac{9}{10}-\frac{2}{40}=0,9-0,05=0,85
e)
(-0,1)^4*20^3+(1\frac{1}{2})^3:(-0,3)^2=\frac{1}{10000}*8000+(\frac{3}{2})^3:(-\frac{3}{10})^2=\frac{8}{10}+\frac{27}{8}*\frac{100}{9}=\frac{8}{10}+\frac{3}{2}*25=0,8+\frac{75}{2}=0,8+37,5=38,3