Odpowiedź:
[tex]a)\ \ \dfrac{125\cdot15}{3^3\cdot5^4}=\dfrac{5^3\cdot3^1\cdot5^1}{3^3\cdot5^4}= \dfrac{\not5^4\cdot3^1}{3^3\cdot\not5^4}=\dfrac{3^1}{3^3}=3^{1-3}=3^{-2}=(\frac{1}{3})^2=\frac{1}{9}\\\\\\\\c)\ \ \dfrac{9^3\cdot4^4}{6^1^0}=\dfrac{9^3\cdot4^3\cdot4}{6^1^0}=\dfrac{(9\cdot4)^3\cdot4}{6^1^0}=\dfrac{36^3\cdot4}{6^1^0}=\dfrac{(6^2)^3\cdot4}{6^1^0}=\dfrac{6^6\cdot4}{6^1^0}=\dfrac{4}{6^{10-6}}=\\\\\\=\dfrac{4}{6^4}=\dfrac{4}{1296}=\dfrac{1}{324}[/tex]
[tex]e)\ \ \dfrac{(8^5\cdot4^3)\cdot25^2}{10^4\cdot2^1^0}=\dfrac{[(2^3)^5\cdot(2^2)^3]\cdot(5^2)^2}{5^4\cdot2^4\cdot2^1^0}=\dfrac{(2^1^5\cdot2^6)^2\cdot\not5^4}{\not5^4\cdot2^4\cdot2^1^0}=\dfrac{(2^2^1)^2}{2^4\cdot2^1^0}=\dfrac{2^4^2}{2^1^4}=\\\\\\=2^{42-14}=2^{28}[/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{2^1^2\cdot6^8}{6^3\cdot2^6}=\dfrac{2^{12-6}\cdot6^8}{6^3}=\dfrac{2^6\cdot6^8}{6^3}=2^6\cdot6^{8-3}=\\\\\\=2^6\cdot6^5=2\cdot2^5\cdot6^5=2\cdot(2\cdot6)^5=2\cdot12^5[/tex]
