[tex]\it \sqrt{3^5\cdot5^3}:\sqrt{3\cdot5}=\sqrt{(3^5\cdot5^3):(3\cdot5)}=\sqrt{\dfrac{3^5\cdot5^3}{3\cdot5}}=\sqrt{\dfrac{3^5}{3}\cdot\dfrac{5^3}{5}}=\\ \\ \\ =\sqrt{(3^5:3)\cdot(5^3:5)}=\sqrt{3^{5-1}\cdot5^{3-1}}=\sqrt{3^4\cdot5^2}=\sqrt{3^4}\cdot\sqrt{5^2}=\\ \\ \\ =\sqrt{3\cdot3\cdot3\cdot3}\cdot\sqrt{5\cdot5}=\sqrt{81}\cdot\sqrt{25}=9\cdot5=45[/tex]
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[tex]\it -\sqrt{512}:\sqrt{2^5}=-\sqrt{512}:\sqrt{2\cdot2\cdot2\cdot2\cdot2}=-\sqrt{512}:\sqrt{32}=\\ \\ \\ =-\sqrt{512:32}=-\sqrt{16}=-4[/tex]
