ZADANIE 1: [latex](4^5cdot x+32^2)cdot 2^5=2^{16}cdot x\ ((2^2)^5cdot x+(2^5)^2)cdot 2^5=2^{16}cdot x\ (2^{10}cdot x+2^{10})cdot 2^5=2^{16}cdot x\ 2^{15}cdot x+2^{15}=2^{16}cdot x\ 2^{16}cdot x-2^{15}cdot x=2^{15}\ 2^{15}(2x-1)=2^{15}\ 2x-1=1\ 2x=2\ x=1\[/latex] ZADANIE 2: [latex][(frac{25}{36})^{-1,5}cdot(1frac15)^frac25cdot(frac56)^{-frac34}]^frac14=\ =[(frac{36}{25})^frac32cdot(frac65)^frac25cdot(frac65)^frac34]^frac14=\ =[(frac65)^3cdot(frac65)^frac25cdot(frac65)^frac34]^frac14=\ =[(frac65)^{3+frac25+frac34}]^frac14=\ =[(frac65)^{3+frac{8}{20}+frac{15}{20}}]^frac14=\ =[(frac65)^{frac{83}{20}}]^frac14=\ =(frac65)^frac{83}{80}[/latex] ZADANIE 3. [latex]frac{4cdot (sqrt2)^{-1}}{sqrt[6]{8}cdotsqrt{sqrt2}}=0,5^{-1,125}\ \ L=frac{2^2cdot (2^frac12)^{-1}}{sqrt[6]{2^3}cdotsqrt{2^frac12}}\ L=frac{2^2cdot2^{-frac12}^}{{2^frac36}cdot2^frac14}}\ L=frac{2^{2-frac12}}{2^{frac12+frac14}}\ L=frac{2^frac32}{2^frac34}\ L=2^{frac32-frac34}\ L=2^{frac64-frac34}\ L=2^frac34\ L=0,5^{-frac34}\ L=0,5^{-0,75} [/latex] Zadanie powyższe albo: a) bęłdnie przpisane b) zawiera błąd w składni zadania.
