Odpowiedź:
[tex]a)\ \ \dfrac{64^6\cdot4^{-7}}{16^5:8^3}=\dfrac{(2^6)^6\cdot(2^2)^{-7}}{(2^4)^5:(2^3)^3}=\dfrac{2^{36}\cdot2^{-14}}{2^{20}:2^9}=\dfrac{2^{36+(-14)}}{2^{20-9}}=\dfrac{2^{36-14}}{2^{11}}=\dfrac{2^2^2}{2^{11}}=\\\\\\=2^{22-11}=2^{11}=2048[/tex]
[tex]b)\ \ \dfrac{27^9:81^3}{243^4}=\dfrac{(3^3)^9:(3^4)^3}{(3^5)^4}=\dfrac{3^{27}:3^{12}}{3^{20}}=\dfrac{3^{27-12}}{3^{20}}=\dfrac{3^{15}}{3^{20}}=3^{15-20}=3^{-5}=\\\\=(\frac{1}{3})^5=\frac{1}{243}\\\\\\c)\ \ \dfrac{125^8\cdot25^3}{625^2}=\dfrac{(5^3)^8\cdot(5^2)^3}{(5^4)^2}=\dfrac{5^{24}\cdot5^6}{5^8}=\dfrac{5^{24+6}}{5^8}=\dfrac{5^3^0}{5^8}=5^{30-8}=5^{22}[/tex]
[tex]d)\ \ \dfrac{5^{12}+5^{13}+5^{14}}{31}=\dfrac{5^1^2+5\cdot5^{12}+5^2\cdot5^{12}}{31}=\dfrac{5^{12}\cdot(1+5+5^2)}{31}=\dfrac{5^{12}\cdot(6+25)}{31}=\\\\=\dfrac{5^1^2\cdot\not31}{\not31}=5^{12}\\\\\\e)\ \ \dfrac{14^7}{4^6\cdot7^7}=\dfrac{2^7\cdot\not7^7}{(2^2)^6\cdot\not7^7}=\dfrac{2^7}{2^{12}}=2^{7-12}=2^{-5}=(\frac{1}{2})^5=\frac{1}{32}[/tex]
[tex]f)\ \ 4\frac{2}{3}-2\frac{1}{2}\cdot3\frac{1}{4}=4\frac{2}{3}-\frac{5}{2}\cdot\frac{13}{4}=\frac{14}{3}-\frac{65}{8}=\frac{112}{24}-\frac{195}{24}=-\frac{83}{24}=-3\frac{11}{24}[/tex]
