Вычислить: $\sqrt[3]{-8}$; $\sqrt[15]{-1}$; $\sqrt[3]{-\frac{1}{27}}$; $\sqrt[5]{-1024}$; $\sqrt[3]{-343}$; $\sqrt[7]{-8^7}$; $\sqrt[3]{343 \cdot 0,125}$; $\sqrt[3]{512 \cdot 216}$;

8) Вычислить: - $\sqrt[3]{-8} = -2$ - $\sqrt[15]{-1} = -1$ - $\sqrt[3]{-\frac{1}{27}} = -\frac{1}{3}$ - $\sqrt[5]{-1024} = -4$ - $\sqrt[3]{-343} = -7$ - $\sqrt[7]{-8^7} = -8$ - $\sqrt[3]{343 \cdot 0,125} = \sqrt[3]{343} \cdot \sqrt[3]{0,125} = 7 \cdot 0,5 = 3,5$ - $\sqrt[3]{512 \cdot 216} = \sqrt[3]{512} \cdot \sqrt[3]{216} = 8 \cdot 6 = 48$ - $\sqrt[5]{32 \cdot 100000} = \sqrt[5]{32} \cdot \sqrt[5]{100000} = 2 \cdot 10 = 20$ - $\sqrt[3]{5^3 \cdot 7^3} = 5 \cdot 7 = 35$ - $\sqrt[4]{11^4 \cdot 3^4} = 11 \cdot 3 = 33$ - $\sqrt[5]{(0,2)^5 \cdot 8^5} = 0,2 \cdot 8 = 1,6$ - $\sqrt[7]{(\frac{1}{3})^7 \cdot 21^7} = \frac{1}{3} \cdot 21 = 7$ - $\sqrt[3]{2 \cdot 500} = \sqrt[3]{1000} = 10$ - $\sqrt[3]{0,2 \cdot 0,04} = \sqrt[3]{0,008} = 0,2$ - $\sqrt[4]{324 \cdot 4} = \sqrt[4]{1296} = 6$ - $\sqrt[5]{2 \cdot 16} = \sqrt[5]{32} = 2$ - $\sqrt[5]{3^{10} \cdot 2^{15}} = (3^{10})^{1/5} \cdot (2^{15})^{1/5} = 3^2 \cdot 2^3 = 9 \cdot 8 = 72$ - $\sqrt[3]{2^3 \cdot 5^6} = 2 \cdot 5^2 = 2 \cdot 25 = 50$ - $\sqrt[4]{3^{12} \cdot (\frac{1}{3})^8} = 3^3 \cdot (\frac{1}{3})^2 = 27 \cdot \frac{1}{9} = 3$ - $\sqrt[10]{4^{30} \cdot (\frac{1}{2})^{20}} = 4^3 \cdot (\frac{1}{2})^2 = 64 \cdot \frac{1}{4} = 16$ - $\sqrt[5]{32} - 0,5 \cdot \sqrt[3]{-216} = 2 - 0,5 \cdot (-6) = 2 + 3 = 5$ - $-\frac{1}{4} \cdot \sqrt[4]{81} + \sqrt[4]{625} = -\frac{1}{4} \cdot 3 + 5 = -0,75 + 5 = 4,25$ - $\sqrt[3]{-1000} - \frac{1}{4} \cdot \sqrt[4]{256} = -10 - \frac{1}{4} \cdot 4 = -10 - 1 = -11$ - $\sqrt[5]{\frac{1}{243}} + \sqrt[3]{-0,001} - \sqrt[4]{0,0016} = \frac{1}{3} - 0,1 - 0,2 = 0,333 - 0,3 = 0,033$ (или $\frac{1}{30}$) 9) Упростить выражение: - $\sqrt[3]{64x^3z^6} = 4xz^2$ - $\sqrt[4]{a^8b^{12}} = a^2|b^3|$ - $\sqrt[5]{32x^{10}y^{20}} = 2x^2y^4$ - $\sqrt[6]{a^{12}b^{18}} = a^2|b^3|$ - $(\sqrt{a} \cdot \sqrt[3]{b})^6 = (a^{1/2} \cdot b^{1/3})^6 = a^3b^2$ - $(\sqrt[3]{a^2} \cdot \sqrt[4]{b^3})^{12} = (a^{2/3})^{12} \cdot (b^{3/4})^{12} = a^8b^9$ - $(\sqrt[3]{a^2 \cdot b})^6 = (a^{2/3} \cdot b^{1/3})^6 = a^4b^2$ - $(\sqrt[3]{27a^3})^4 = (3a)^4 = 81a^4$ - $(\sqrt[3]{x})^6 \cdot (\sqrt[3]{y^2})^3 = x^2 \cdot y^2$ - $\sqrt[4]{ab} \cdot \sqrt[4]{a^3c} = \sqrt[4]{a^4bc} = |a| \cdot \sqrt[4]{bc}$ - $\sqrt[3]{16a} \cdot \sqrt[3]{\frac{1}{2ab}} = \sqrt[3]{\frac{16a}{2ab}} = \sqrt[3]{\frac{8}{b}} = \frac{2}{\sqrt[3]{b}}$ - $\sqrt[5]{a^6b^7} : \sqrt[5]{ab^2} = \sqrt[5]{\frac{a^6b^7}{ab^2}} = \sqrt[5]{a^5b^5} = ab$ - $\sqrt[3]{81x^4y} : \sqrt[3]{3xy} = \sqrt[3]{\frac{81x^4y}{3xy}} = \sqrt[3]{27x^3} = 3x$ - $\sqrt[3]{\frac{3x}{y^2}} : \sqrt[3]{\frac{y}{9x^2}} = \sqrt[3]{\frac{3x}{y^2} \cdot \frac{9x^2}{y}} = \sqrt[3]{\frac{27x^3}{y^3}} = \frac{3x}{y}$ - $\sqrt[3]{2ab} \cdot \sqrt[3]{4a^2b} = \sqrt[3]{8a^3b^2} = 2a\sqrt[3]{b^2}$ - $\sqrt[4]{3a^2b^3} \cdot \sqrt[4]{27a^2b} = \sqrt[4]{81a^4b^4} = 3|ab|$ - $\sqrt[4]{\frac{2b}{a^3}} : \sqrt[4]{\frac{a}{8b^3}} = \sqrt[4]{\frac{2b}{a^3} \cdot \frac{8b^3}{a}} = \sqrt[4]{\frac{16b^4}{a^4}} = \frac{2|b|}{|a|}$