Odpowiedź i szczegółowe wyjaśnienie:
[tex]a)\ \dfrac{125\cdot15}{3^3\cdot5^4}=\dfrac{5^3\cdot5\cdot3}{3^3\cdot5^4}=\dfrac{5^{3+1}\cdot3}{3^3\cdot5^4}=\dfrac{5^4\cdot3}{3^3\cdot5^4}=\dfrac{3}{3^3}=3^{1-3}}=3^{-2}\\\\\\b)\ \dfrac{(3^5)^4\cdot6^4}{9^7\cdot 4^2}=\dfrac{3^{20}\cdot(3\cdot2)^4}{(3^2)^7\cdot(2^2)^2}=\dfrac{3^{20}\cdot 3^4\cdot 2^4}{3^{14}\cdot 2^4}=\dfrac{3^{24}}{3^{14}}=3^{20-14}=3^{10}[/tex]
[tex]c)\ \dfrac{9^3\cdot4^4}{6^{10}}=\dfrac{(3^2)^3\cdot(2^2)^4}{(3\cdot2)^{10}}=\dfrac{3^6\cdot2^8}{3^{10}\cdot2^{10}}=3^{6-10}\cdot2^{8-10}=3^{-4}\cdot2^{-2}=\dfrac{1}{3^4\cdot 2^2}[/tex]
[tex]d)\ \dfrac{0,25^3:0,5^3}{5^3}=\dfrac{(0,25:0,5)^3}{5^3}=\dfrac{(\dfrac14\cdot2)^3}{5^3}=\dfrac{0,5^3}{5^3}=(\dfrac{0,5}{5})^3=0,1^3[/tex]
[tex]e)\ \dfrac{(8^5\cdot4^3)^2\cdot25^2}{10^4\cdot2^{10}}=\dfrac{((2^3)^5\cdot(2^2)^3)^2\cdot(5^2)^2}{(5\cdot2)^4\cdot2^{10}}=\dfrac{(2^{15}\cdot2^6)^2\cdot 5^4}{5^4\cdot2^4\cdot2^{10}}=\\\\=\dfrac{(2^{21})^2}{2^{14}}=\dfrac{2^{42}}{2^{14}}=2^{41-14}=2^{27}[/tex]
[tex]f)\ \dfrac{64^2\cdot36^4}{6^3\cdot2^6}=\dfrac{(2^6)^2\cdot(6^2)^4}{6^3\cdot2^6}=\dfrac{2^{12}\cdot6^8}{6^3\cdot2^6}=2^{12-6}\cdot6^{8-3}}}=2^6\cdot6^5=\\\\=2^6\cdot(2\cdot3)^5=2^6\cdot2^5\cdot3^5=2^{11}\cdot 3^5[/tex]
